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| − | <div class="container-full"> | + | <div class="container-full"> |
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| | <div class="card"> | | <div class="card"> |
| − | <img class="card-img-top" src="img/T--SZU-China--pre_design.jpg" /> | + | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/f/fc/T--SZU-China--Model-home.jpg" /> |
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| − | <div class="row" style="background-image: url();"> | + | <div class="col-10 offset-1 shadow"> |
| − | <div class="col- 9 offset-1 shadow border-top "> | + | |
| − | <div class="text-center">
| + | <div class=" text-center"> |
| − | <h1 id="header">Epidemic Model</h1>
| + | <h1 class="h1" style="color: #469789; text-align: center;">Model</h1> |
| − | </div>
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| − | <h2>Introduction</h2>
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| − | <p>We developed a mathematical epidemic model to predict the population dynamics of cockroaches infected by our Metarhizium anisopliae. We then performed numerical simulations on the model and sensitivity analysis on some key parameters. By doing so,
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| − | <b>
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| − | we expected to estimate the efficiency with lethal time after using our ‘cockroach terminator’ indoors, and analyzed the impact of each relative factors that influence our product so as to modify our design</b>.</p>
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| − | </div>
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| − | <h2>Natural condition</h2>
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| − | <p>In natural condition indoors, due to environmental resistance like food, water and space, the population of cockroaches is more likely to follow a S-shaped growth curve (sigmoid growth curve), which can be formalized mathematically by logistic function $\dfrac {dN}{dt}=rN\left( 1-\dfrac {N}{K}\right)$ .After we research papers and government researches, we found that
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| − | </p>
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| − | <div class="card border-success" style="border-color: #469789;">
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| − | The average number of cockroach in Shenzhen family house is 38 The grow rate (r) is 0.61, And by assumption, we set the carrying capacity (K) to be 40.
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| − | </div>
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| − | <p>After simulating the numerical solution (Figure 1), we can see that the cockroach population growing rapidly and reach to stationary state of 40 less than fifteen days. It’s necessary for as to control this worrisome infection.
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/a/a0/T--SZU-China--Model_E_1.png" />
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| − | </div>
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| − | <p class="text-center" style="color: #A29F9F;">Figure 1: The population growth curve of cockroaches in house from one to large amount.</p>
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| − | </div>
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| − | </div>
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| − | <h2>After control</h2>
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| − | <p>After we using M.anisopliae emulsifiable powder to control the cockroach population indoors, M.anisopliae will behave like a disease and spread out inside the population and finally kill the cockroaches. Our SID epidemic model with ordinary differential equation (ODE) was constructed based on SIR (Susceptible, Infectious, Recovered) epidemic model, following are some basic properties and assumptions of our model.
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| − | </p>
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| − | </div>
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| − | | + | |
| − | <!--Assumptions-->
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| − | <div class="indent">
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| − | <h2 id="Assumptions">Assumptions</h2>
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| − | <ul>
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| − | <li>1. The number of cockroach has reached the highest value in stable stage</li>
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| − | <li>2. Ignore natural birth and death rates in our system</li>
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| − | <li>3. Infectious individuals can not recover</li>
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| − | <li>4. Other factors that may affect the experiment are ignored</li>
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| − | </ul>
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| − | </div>
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| − | <hr>
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| − | <!--With infection-->
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| − | <div class="indent">
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| − | <h2 id="With infection">With infection</h2></div>
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/d/d8/T--SZU-China--HP_Model_6.png" />
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| − | </div>
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| − | <p class="text-center">Figure 2: Diagram of epidemic model. Showing the relation between each group of individual.</p>
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| − | </div>
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| − | <p>Our model was constructed based on SIR epidemic model (Susceptible, Infectious, Recovered) , following are some basic properties:</p>
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| − | <ul>
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| − | <li>1.The population growth of cockroach follows sigmoid growth curve.</li>
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| − | <li>2.The population of cockroach has reached close to the stationary stage.</li>
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| − | <li>3.Ignore natural death rate in our system since stubborn vitality of cockroach.</li>
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| − | <li>4.Infectious individuals can not recover, and ignore they give birth.
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| − | </li>
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| − | <li>5.Naturally all cockroaches are susceptible individuals, they can infect by M.anisopliae becoming infectious individuals.
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| − | </li>
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| − | <li>
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| − | 6.The number of individual being infected in a contact between a susceptible and an infectious subject is determined by standard incidence rate $\dfrac {\beta IS}{S+I}$ .
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| − | </li>
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| − | <li>7.The transition rate between infectious and dead is γ, its reciprocal ($\dfrac {1}{\gamma}$) determines the average infectious period, which is estimate by experiment data.
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| − | </li>
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| − | <li>
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| − | 8.Other factors that may affect the experiment are negligible.
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| − | </li>
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| − | </ul>
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| − | </div>
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| − | <hr>
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| − | <!--Parameters-->
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| − | <div class="row">
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| − | <h2 id="Parameters">Parameters</h2>
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| − | <table class="table table-bordered">
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| − | <thead>
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| − | <tr class="table-active text-center">
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| − | <th>Parameter</th>
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| − | <th>Value</th>
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| − | <th>Meaning</th>
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| − | <th>Source</th>
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| − | </tr>
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| − | </thead>
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| − | <tbody>
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| − | <tr>
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| − | <td>β</td>
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| − | <td>0.775</td>
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| − | <td>transmission rate, which is the probability of getting the infection in a contact between susceptible and an infectious
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| − | </td>
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| − | <td>[2] [3]</td>
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| − | </tr>
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| − | <tr>
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| − | <td>γ</td>
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| − | <td>1/7</td>
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| − | <td>mortality, which is the the transition rate between I and D, its reciprocal (1/γ) determines the average infectious period
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| − | </td>
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| − | <td>B</td>
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| − | </tr>
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| − | <tr>
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| − | <td>r</td>
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| − | <td>0.61 d<sup>-1</sup></td>
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| − | <td>growth rate</td>
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| − | <td>[1]</td>
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| − | </tr>
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| − | <tr>
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| − | <td>K</td>
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| − | <td>40</td>
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| − | <td>carrying capacity</td>
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| − | <td>A</td>
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| − | </tr>
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| − | <tr>
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| − | <td>S(t)</td>
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| − | <td>variable</td>
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| − | <td>the number of susceptible individuals over time</td>
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| − | <td>-</td>
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| − | </tr>
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| − | <tr>
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| − | <td>I(t)</td>
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| − | <td>variable</td>
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| − | <td>the number of infectious individuals over time</td>
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| − | <td>-</td>
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| − | </tr>
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| − | <tr>
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| − | <td>D(t)</td>
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| − | <td>variable</td>
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| − | <td>the number of dead individuals over time</td>
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| − | <td>-</td>
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| − | </tr>
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| − | <tr>
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| − | <td>N(t)</td>
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| − | <td>S(t)+I(t)+D(t)</td>
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| − | <td>population size</td>
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| − | <td>-</td>
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| − | </tr>
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| − | <tr>
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| − | <td>S(0)</td>
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| − | <td>35</td>
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| − | <td>the initial number of susceptible individuals</td>
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| − | <td>A</td>
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| − | </tr>
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| − | <tr>
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| − | <td>I(0)</td>
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| − | <td>3</td>
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| − | <td>the initial number of infectious individuals</td>
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| − | <td>-</td>
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| − | </tr>
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| − | <tr>
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| − | <td>D(0)</td>
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| − | <td>0</td>
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| − | <td>the initial number of dead individuals</td>
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| − | <td>-</td>
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| − | </tr>
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| − | <tr>
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| − | <td colspan="4" class="text-left">
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| − | <sup>[]</sup>See in the reference code at the bottom<br>
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| − | <sup>A</sup>Government researches from Shenzhen Center for Disease Control and prevention<br>
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| − | <sup>B</sup>Estimate by experimental data
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| − | </td>
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| − | </tr>
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| − | </tbody>
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| − | </table>
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| − | <div class="indent">
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| − | <p class="text-center">Table 1: Parameters and variables for the model, all value are from research papers or experimental date
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| − | </p>
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| − | </div>
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| − | </div>
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| − | <div class="row">
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| − | <p>By the above relations between each group of number, the system based on assumption described above can be expressed by the following set of ordinary differential equations:
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| | + | <p style="font-size: 18px; font-weight: bold;"> |
| | + | On this page, two mathematical models were constructed to analysis the efficiency of our producet based on simulation and experiment. <br />Click the frame to see the details. |
| | + | </p> |
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| − | $$\dfrac {dS}{dt}=rN\left( 1-\dfrac {N}{K}\right) -\dfrac {\beta IS}{S+I}$$ $$\dfrac {dI}{dt}=\dfrac {\beta IS}{S+I}-\gamma I$$ $$\dfrac {dD}{dt}=\gamma I$$ $$N=S+I+D$$
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| − | This system is non-linear, and the analytic solution does not exist, but we can compute the numerical solution.
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| − | </p>
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| − | <p>We used improved Euler method to estimate the discrete solution in one step size to simulate the change of number with time in days (see the results). And Runge-Kutta methods solution for variable-step by MATLAB to constructed the sensitivity analysis.
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| − | </p>
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| | </div> | | </div> |
| − | <hr>
| + | </div> |
| − | <!--Results-->
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| − | <div class="indent">
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| − | <h2 id="Results">Results</h2>
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| − | <p>The following curves (Figure 3) show dynamics of number change of each kinds of individuals.
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| − | </p>
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| − | <p>
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| − | We see that the infectious individuals grow fast before first 7 day, and then began to drop. The total number of cockroaches continuously going down.
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| − | </p>
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| − | <p>
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| − | We specify the median lethal time (LT50), which means 50% of cockroaches dead, where in this condition is about 8 day, and lethal time 80% (LT80) is about 15 day. This result is reasonable with our expectation, it proved that our product indeed control the total number of cockroaches efficiently in doors.
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| − | <div class=" col-6 offset-3"> | + | |
| − | <div class="card">
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/c/cd/T--SZU-China--Model_E_3.png" />
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| − | </div>
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| − | <p class="text-center" style="color: #A29F9F;">
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| − | Figure 3: The epidemic model simulating change of each group of individual within 40 days.
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| − | </p>
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| − | </div>
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| − | <hr>
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| | <div class="row"> | | <div class="row"> |
| − | <h2 id="Sensitivity Analysis">Sensitivity Analysis</h2>
| + | <div class="col-4 offset-1"> |
| − | <p>We use sensitivity analysis to analyze the impacts of some important parameter values (β, γ) on our model outcomes lethal time 50% and 80% (LT50 and LT80), in order to figure out what we should need to improve in future, and which parameters we need to be more certain.
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| − | </p>
| + | <div id="card1" class="card border-3 h-100"> |
| − | <div class="col-6"> | + | <div class=" view text-center"> |
| − | <p>We ran our model with transmission rate (β) and mortality (γ) ranging from 0 to 1 and plotted these values against the time in LT50 and LT80. What’s more, we introduced sensitivity coefficient (△t*p/t *△p ratio of the relative change of the lethal time to the relative change of the parameter) into consideration, increasing our parameters 10 percent, and find the relative change of the lethal time. The figures below show the changing tendency of lethal time with respect to each parameter and the sensitivity coefficient in ten percent up. | + | <img id="icon" class="card-img-top " style="width: 96px;" src="https://static.igem.org/mediawiki/2018/ 4/ 48/T--SZU-China-- Model_home1.png"/ > |
| − | </p> | + | </div> |
| − | </div>
| + | <div class="card-body text-center"> |
| − | | + | <a style="color: #469789;" href="https://2018.igem.org/Team:SZU-China/Epidemic_Model"><h3 >Epidemic Model </h3></a> |
| − | | + | <p class="card-text" >We developed a epidemic model with ordinary differential equation to predict the population dynamics of cockroaches infected by Metarhizium anisopliae. We then performed numerical simulations on the model and sensitivity analysis on some key parameters to find they impacts. |
| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/ c/ c1/T--SZU-China-- Model_E_4.png" /> | + | </p> |
| | + | </div> |
| | </div> | | </div> |
| − | <p class="text-center" style="color: #A29F9F;">Figure 4: Change of the lethal time when transmission rate (β) ranging from 0 to 1. Blake dot represent our parameter used in Table 1.
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| − | </p>
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/8/8e/T--SZU-China--Model_E_5.png" />
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| − | </div>
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| − | <p class="text-center" style="color: #A29F9F;">Figure 5: Change of the lethal time when mortality (γ) ranging from 0 to 1. Upper x-axis is 1/γ, indicating the average mortality day. Blake dot represent our parameter used in Table 1, and dash line showing when lager than 0.8 because ODE system can not find solution in our interval.
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| − | </p>
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| | </div> | | </div> |
| − | <div class="col-6">
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| − | <p>We can conclude the intuitive results after scanning either parameter from 0 to 1. For transmission rate (Figure 4), as beta increasing, both LTD50 and LT80 going down. However, the change of lethal time become more smoothly when beta closer to one. The black dot in curves indicates our simulating parameter value 0.775 in epidemic model, which can consider as a good approximation and high efficiency that we do not need to increase so much.
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| − | </p>
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| − | </div>
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| − | </div>
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| − | <div class="row">
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| − | <p>As for mortality (Figure 5), lethal time will increase dramatically when gamma gets closer to zero or one (when gamma closer to one, the ODE system can not find real solution in our interval), but change smoothly in a low region in the middle. That’s sound great for as since the black dot, indicating our simulating parameter value 1/7 in epidemic model, lines near the middle. So, if we can control to increase mortality a little bite, it can make a difference. This is just what we do in our project.
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| − | </p>
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| − | </div>
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| − | <div class="col-6">
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| − | <div class="card">
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/3/38/T--SZU-China--Model_E_6.png" />
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| − | </div>
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| − | <p class="text-center" style="color: #A29F9F;">Figure 6: Sensitivity coefficient of transmission rate (β) and mortality (γ) to LT50 and LT80.
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| − | </p>
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| − | </div>
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| − | <p>Moreover, the sensitivity coefficient in Figure 6 shows the coefficient is less than -0.8, which indicate a low sensitivity of beta and gamma, while gamma has higher sensitivity compared with beta. In conclusion, the parameters we estimated previously did not greatly affect the lethal time of our model, we can say our parameters are well approximate.
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| − | </p>
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| − | </div>
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| − | <div class="indent">
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| − | <h2>Discussion</h2>
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| − | <p>By our improved epidemic model, we successfully predict the population dynamics of cockroaches infected by our <i>Metarhizium anisopliae</i> indoors. Estimate the key parameters beta to be 0.775, gamma to be 1/7, can be considered as a good approximation not only we estimate them from research papers and experimental data, but also we constructed sensitivity analysis to these parameters and showed a low sensitivity. These results give us a clear relation about each factor and to direct our project design. Numerical simulations on the model showed our product kill cockroaches indoors with a lethal time 50% (LT50) about 8 day, and lethal time 80% (LT80) about 15 day. Thanks to the assumption, we can simplify our model, however in future, we will consider more factor that may influence our prediction to make our model more real.
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| − | </p>
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| − | </div>
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| − | <div class="indent">
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| − | <h2>References</h2>
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| − | <div class="row">
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| − | <p>
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| − | [1] D. M. Müller-Graf, Jobet, E., Cloarec, A., Rivault, C., Baalen, M. V., & Morand, S. (2001). Population dynamics of host-parasite interactions in a cockroach-oxyuroid system. Oikos, 95(3), 431–440.
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| − | </p>
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| − | <p>
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| − | [2] Campaña, Ana & Funderburk, Karen & Kaur, Amandeep & Puente, Patricia & Ríos-Soto, Karen. (2017). A Household Model of Cockroach Infestation and Its Effects on Atopic Asthma Symptoms.
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| − |
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| − | </p>
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| − | <p>
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| − | [3] Ni, Yu-Ting, et al. (2014). Metarhizium anisopliae as a Potential Microbial Agent for Managing the Brown-banded Cockroach, Supella longipalpa (F.).
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| − |
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| − | </p>
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| − | <p>
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| − | [4] Hu, Z., Liu, S., & Wang, H. (2008). Backward bifurcation of an epidemic model with standard incidence rate and treatment rate. Nonlinear Analysis Real World Applications, 9(5), 2302-2312.
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| − | </p>
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| − | </div>
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| − | <!--Model2-->
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| − | <div class="indent">
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| − | <h1 style="color: #469789;">Statistic Model</h1>
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| − | </div>
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| − |
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| − | <div class="row">
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| − | <h2>Introduction</h2>
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| − | <p>
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| − | Statistic analysis can give us a clear and scientific understanding of our complex data, that was the reason why we construct a statistical model for our experimental data.
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| − |
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| − | </p>
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| − | <p>
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| − | The data from simulating room were subjected to statistic analysis to determine whether there are significantly different in migration rate, mortality and gnawing rate using
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| − | <i>One-way ANOVA</i>.
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| − | <font color="#469789">Levene’s test</font> to determine whether each group is homogeneity, then
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| − | <font color="#469789">T-test</font> for pooled data in pairwise gave us the value and finally to evaluate significant difference.
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| − |
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| − | </p>
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| − | </div>
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| − | <div class="indent">
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| − | <h2>Levene’s test</h2>
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| − | <p>Levene’s test is used to assess the equality of variances for a variable from two or more groups. In our model, we have four independent groups. Since in the following procedures for T-test, we assume that the variances of the populations from four samples are equal, so we need to test whether the following variances can be assume to be equal.</p>
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| − |
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| − | </div>
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| − | <div class="indent">
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| − | <h4>Assumptions:</h4>
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| − | <p>
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| − | <font color="#469789">1. Due to the advantage of Levene’s test, we do not need to assume the normal data
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| − | </font>
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| − | </p>
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| − | <p>
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| − | <font color="#469789">2. Null hypothesis that all populations from samples have the same variances
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| − | </font>
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| − | $$ H_{0}:\sigma _{1}=\sigma _{2}=\cdots \sigma _{k}, \quad H_{A}:\sigma _{i}\neq \sigma _{j}, \quad \alpha =0.05 $$
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| − | </p>
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| − | <p>The Levene Statistic (W) of each groups is calculated by: $$ W{=}\dfrac {\left( N-k\right) }{\left( k-1\right) } \dfrac {\sum ^{k}_{i=1}N_{i}\left( Z_{i\cdot}-Z_{i\cdot\cdot}\right) ^{2}} {\sum ^{k}_{i=1}\sum ^{N_{i}}_{j=1}\left( Z_{ij}-Z_{i\cdot}\right) ^{2}} \sim F\left( \alpha ,k-1,N-k\right) $$
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| − | </p>
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| − | <p>Where</p>
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| − |
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| − | <ul>
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| − | <li> $k$ is the number of groups which need to be tested, equal to 4 in our data
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| − | </li>
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| − | <li>$N_{i}$ is the number of cases in the ith group</li>
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| − | <li>$N$ is the total number of cases in all groups, equal to 12 in our data</li>
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| − | <li>$Y_{ij}$ is the value of the measured variable for the $i$th case from the $j$th group</li>
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| − | <li>$Z_{ij}=\left| Y_{ij}-\overline {Y_{i}}\right|$, $\overline {Y_{i}}$ is the mean of the $i$th group</li>
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| − | <li>$\overline {Z_{i\cdot}}$ is the mean of the $Z_{ij}$ for group $i$</li>
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| − | <li>$\overline {Z_{\cdot\cdot}}$ is the mean of all data</li>
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| − | </ul>
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| − | <div class="indent">
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| − | <p>After calculate Levene Statistic of each group with SPSS, the W value are shown below:</p>
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| − | <table class="table">
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| − | <caption>Test of Homogeneity of Variances</caption>
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| − | <thead>
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| − | <tr>
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| − | <th scope="col"></th>
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| − | <th scope="col">Levene Statistic</th>
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| − | <th scope="col">df1</th>
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| − | <th scope="col">df2</th>
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| − | <th scope="col">Sig.</th>
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| − | </tr>
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| − | </thead>
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| − | <tbody>
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| − | <tr>
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| − | <th scope="">Migration Rate</th>
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| − | <td>2.070</td>
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| − | <td>3</td>
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| − | <td>8</td>
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| − | <td>.183</td>
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| − | </tr>
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| − | <tr>
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| − | <th scope="">Mortality</th>
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| − | <td>3.122</td>
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| − | <td>3</td>
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| − | <td>8</td>
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| − | <td>.088</td>
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| − | </tr>
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| − | <tr>
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| − | <th scope="">Gnawing Rate</th>
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| − | <td>.000</td>
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| − | <td>3</td>
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| − | <td>3</td>
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| − | <td>1.000</td>
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| − | </tr>
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| − | </tbody>
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| − | </table>
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| − | </div>
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| − |
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| − | </div>
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| − |
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| − | <div class="indent">
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| − | <p>
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| − | Fortunately, all
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| − | <font color="#469789">$ W < F\left( 0.05,3,8\right) =4.066 $ or Sig.>0.05</font>, indicating the null hypothesis is accepted, meaning
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| − | <font color="#469789">$ \sigma _{1},\sigma _{2},\sigma _{3},\sigma _{4} $,</font>
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| − | do not have statistically different, so we can say they have the same variance σ2, and we can continues our procedure.
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| − |
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| − | </p>
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| − | </div>
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| − |
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| − | <div class="indent">
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| − | <h2>T-test for pooled data</h2>
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| − | <p>The independent T-test for pooled data is used to determine whether the mean difference between two groups is statistically significantly different
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| − | </p>
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| − | <h5>
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| − | Assumptions:
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| − | </h5>
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| − | <p style="color: #469789;">1.The sample groups are pairwise independent</p>
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| − | <p style="color: #469789;">2.All populations from samples have the same variances</p>
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| − | <p>The T-value (t) of eachpair is calculated by:$$t_{n_{1}+n_{2}-2}=\dfrac { \overline {x_{1}}-\overline {x_{2}}}
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| − | {\sqrt {\dfrac {\left( n_{1}-1\right) s^{2}_{1}+\left( n_{2}-1\right) s^{2}_{2}}
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| − | {\left( n_{1}-1\right) + \left( n_{2}-1\right) }\left( \dfrac {1}{n_{1}}+\dfrac {1}{n_{2}}\right) }}$$ </p>
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| | | | |
| | + | <div class="col-4 offset-2 "> |
| | + | <div id="card2" class="card border-3 h-100"> |
| | + | <div class="view text-center"> |
| | + | <img id="icon" class="card-img-top" style="width: 96px;" src="https://static.igem.org/mediawiki/2018/4/4b/T--SZU-China--Model_home2.png"/> |
| | + | </div> |
| | + | <div class="card-body text-center"> |
| | + | <a style="color: #469789;" href="https://2018.igem.org/Team:SZU-China/Statistic_Model"><h3 >Statistic Model</h3></a> |
| | + | <p class="card-text">We constructed a statistical model for our experimental data from simulating room. It can give us a clear and scientific understanding that whether there had significant difference in migration rate, mortality and gnawing rate between each products.</p> |
| | | | |
| − | </div>
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| − | <div class="indent">
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| − | <p>When $ n_{1}=n_{2}=n=3 $ in this case, it can be simplify as:
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| − | $$ t_{2\left( n-1\right) }=\dfrac {\overline {x_{1}}-\overline {x_{2}}}{\sqrt {\dfrac {s^{2}_{1}+s^{2}_{2}}{n}}} $$
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| − | </p>
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| − |
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| − | </div>
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| − | <div class="indent">
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| − | <p>By using two-tailed test, if p-value is lower than 0.05 or $ t > t_{4,0.05\left( two-tailed \right) }=2.776 $, we can say two mean have statistically significantly different.
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| − | </p>
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| − |
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| − | </div>
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| − |
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| − | <div class="indent">
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| − | <h3>Results</h3>
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| − | <p>Levene’s test, gave us results that each group is homogeneity at P-value of 0.05, indicating we can assume they have equal variances.T-test for pooled data gave us following results:
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| − | </p>
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| − | <p>The graphs in figure 1 divided in matrix cell Zij show the visualized results of above procedures, t value lager than 2.776 showing red means Zi statistically significantly higher than Zj, while lower than -2.776 showing green means Zi statistically significantly lower than Zj. More red or green means different more significantly. Where, Z1, Z2, Z3, Z4 represent cockroach killing chalk, BAYER-Premise, M.anisopliae emulsifiable powder and blank group respectively.
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| − | </p>
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| − | <div class="row">
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| − | <div class="col-5 offset-1">
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| − | <div class="card h-100">
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/0/03/T--SZU-China--S_1.png" />
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| | </div> | | </div> |
| − | </div>
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| − | <div class="col-5 offset-1">
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| − | <div class="card h-100">
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/1/17/T--SZU-China--S_2.png" />
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| − | </div>
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| − | </div>
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| − | <div class="indent">
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| − | <div class="col-6 offset-3">
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| − | <div class="card">
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| − | <img class="card-img-top" src="https://static.igem.org/mediawiki/2018/e/e6/T--SZU-China--S_3.png" />
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| − | </div>
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| − | <p class="text-center" style="color: #A29F9F;">Figure 1: Results of independent T-test for migration rate, mortality and gnawing rate. Matrix cell Zij means Zi compared to Zj. More red or green means different more significantly.
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| − | </p>
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| − |
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| − | </div>
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| | </div> | | </div> |
| | </div> | | </div> |
| | </div> | | </div> |
| − | | + | </div> |
| − | <p>We can obviously see that cockroaches will behave strong migration tendency after people using cockroach killing chalk or BAYER-Premise. Migration rate infected by M.anisopliae emulsifiable powder was significantly lower than that by cockroach killing chalk or BAYER-Premise (P
| + | |
| − | <0.05), even lower than blank group. While, there was no significant difference in migration rate between cockroach killing chalk and BAYER-Premise (P>0.05).
| + | |
| − | </p>
| + | |
| − | <p>
| + | |
| − | Similarly, gnawing rate in M.anisopliae group was significantly higher than that in cockroach killing chalk or BAYER-Premise group (P
| + | |
| − | <0.05), while between the latter two groups, there was no significant difference(P>0.05). Thus, M.anisopliae will spread easier in cockroaches population causing an epidemic-like disease. As for mortality within three days, there was no significant difference between each two groups (P>0.05).
| + | |
| | | | |
| − | </p>
| + | |
| − | <p>
| + | |
| − | The results above show that M.anisopliae emulsifiable powder has higher efficiency than other traditional cockroach-killing methods. It has significantly lower migration rate, higher gnawing rate to spread out naturally, and has similar mortality after using it.
| + | |
| − | </p>
| + | |
| | | | |
| − | </div>
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| − | <div class="indent">
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| − | <h3>References</h3>
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| − | <p>[1] Levene, Howard (1960). “Robust tests for equality of variances”. In Ingram Olkin; Harold Hotelling; et al. Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford University Press. pp. 278–292.</p>
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| − | <p>[2]
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| − | <a href="https://en.wikipedia.org/wiki/Levene%27s_test">https://en.wikipedia.org/wiki/Levene%27s_test</a>
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| − | </p>
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| − | </div>
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