Anthelmintic Use Model

Due to excessive use of anthelmintics against various parasites in cattle, the resistance to anthelmintics in nematodes has grown and has become more extensive than the current situation in horses [1]. In the early stages of our project we knew that the current problems brought by small strongyles were not yet as extensive in Sweden [2]. Therefore we made a model of the growth of nematodes in horses and on pastures, to see the difference between regular use and an optimized use of anthelmintics. The mean usage of anthelmintics in sweden is 3.2 times per year, and there is no common time to use the anthelmintics [3]. However, the treatment occurence that was later used in the model, was information that was retrieved from our own conducted market analysis, which states that the most prevalent use of anthelmintics is two times per year. The optimized use would be to only use anthelmintics when it’s needed, e. g. when the amount of parasites in the horse exceeds a threshold. Some of the variables that the model takes in to account is the usage of anthelmintics and the number of horses, the temperature dependence of the parasite egg to develop into a larva and the numberof horses on a pasture to receive the results.

The model was inspired by a model that looks into how effective anthelmintic treatments are on sheep at pasture [4]. Due to the overuse of anthelmintics in sheep, the efficiency of the medicines have decreased resulting in sheep dying of starvation because of the excessive amount of parasites in the gastro-intestinal area. This causes big economical losses for sheep owners.

With this model we intend to improve our Worm Buster project since it would prevent anthelmintics overuse by determining the optimal amount of treatments. This would be complementary to the Worm Buster, which helps avoid wrong dosage of anthelmintics while treating the horse. In combination both tools help to decrease the overuse of anthelmintics, and thus prevent resistance development.

Design

The model is built upon ordinary differential equations (equation 1 and 2). Matlab is used for the calculation of the model, where Matlab's inbuilt function ode45 is used. The programs that were made and used for the calculations can be found here. At each step of the calculation, the program is looking at given temperature data for a year and other variables that will differ depending on the environment. These variables are described in table 1. Two extreme situations were analyzed, one where a horse has a parasite count that hits the threshold of maximum amount (100 000) of parasites and the second where the horse doesn’t have any parasites (although this is a very unlikely scenario) [5]. The months at which anthelmintics were used in the regular use, was set to April and October, which are two months when it's likely that a horse owner gives anthelmintics to its horse [3]. As mentioned before, the mean value of how many times horses get anthelmintics are 3.2, however in the calculations the chosen value was set to 2, because this was information that was received from our conducted survey. The MATLAB code for the model can be found here.

\(L_t^\prime = (\rho + \beta \cdot H) \cdot L_t + q \cdot \lambda \cdot H \cdot A_t\) (Equation 1)
\(A_t^\prime = d \cdot \beta \cdot L - \mu \cdot A_t - A \cdot u\) (Equation 2)

Table 1. The values and descriptions for the different variables that are used in the model.

Variables	Value	Description
L		Density of infective larvae on one hectare pasture.
A		Mean number of adult parasites per horse
\rho;	0.025 [4]	Rate at which larva is lost from pasture, with other reasons than being eaten by the horses
\beta;(A)	6 or 20	Square metres eaten pasture per day. Normal value is 20, if the amount of parasites in the horse exceeds over the threshold, then the food intake decreases with 70%.
H	1	Horse population density per ha
q(T)	Equation 3	Probability that an egg develops into an larvae, which is temperature, T (C), dependent
\lambda;	54 [4]	Mean rate at which an adult worm produces eggs
d	0.48 [4]	The probability that an ingested larva develops into an adult worm
\mu;	0.03 [4] and 0.99	Mortality rate of adult parasites, normal rate is at 0.03, when anthelmintics are in use, the value increases to 0.99.
u	0 or 1	Binary value that indicates if anthelmintic are used, 0 if not, 1 if used.

Because the development of eggs to larvae is temperature dependent, a linear equation for calculating the probability of an egg to develop into a larva was created. The equation is based on information about how long it takes for an egg to develop into a larva [6]. This equation was created by first dividing all the given temperatures by the highest temperature. A linear regression was made with these values and the temperature. The probability of an egg to develop into a larva in the earlier mentioned study was at 0.0275. If this value is assumed to be the mean probability, then it’s 20 times smaller than the mean probability in this trend line that was received (equation 3). Therefore the constants in the equation was divided with 20 to match it. The temperature data was used was from the Uppsala Aut weather station measurement of mean temperature during 2017 [7].

q = (0.00342 × T − 0.2411) × 0.05 (Equation 3)

β is the amount of square metres grass a horse eats per day. A horse eats approximately five times more than a sheep [8, 9]. Beta decreases if the amount of parasites in the gastrointestinal area of the horse exceeds an amount that is non-detrimental to the horse's health. The model takes into account a 70% decrease in food intake [4]. However, the only information about when a horse should be treated with anthelmintics is based on the egg count in horse feces and not on the amount of parasites in the horse. Therefore an arbitrary threshold was set to 100 000.

The constants μ, mortality rate of adult parasites, the mortality is set to 0.03, when anthelmintics is in use, the mortality changes to 0.99. λ, mean rate at which an adult worm produced eggs and d, the probability of an larva to develop into a adult worm, were the same as in the model that served as inspiration for this one [4].

Results

With the same starting conditions (only varying when anthelmintics is used) four datasets were obtained. The four different data sets show how the density of parasites per hectare pasture and how the amount of parasites per horse varies for both the regular and the optimized use of anthelmintics. As mentioned in the method, two extreme points of starting values were used, which was when L₀, the density of worms per ha pasture, is 1000, and A₀ is either 10000 and 0. The results of the calculations are shown in the graphs (figure 1, 2, 3 and 4).

Figure 1. The amount of parasites per horse where regular and optimized use of anthelmintics is compared. The starting value is 0 parasites in the horse. Every time anthelmintics is used there is a sharp decline in the graph. Over a five year period, the regular use of anthelmintics, would be 10 times. For the optimized use, anthelmintics would be used two times, this is seen in the last year. The amount of parasites in the horse are lower for the regular use of anthelmintics, but that is understandable, because anthelmintics is used more often. However, in the optimized use, the amount of parasites never exceeds a value that would be dangerous for the horse.

Figure 2. How the density of parasites per hectare changes where regular and optimized use of anthelmintics is compared. The starting value of parasites in the horse are set to 0. The data fluctuates because the temperature changes day to day, which affects the development of an egg turning into a larvae. This can also be seen during the summer months, where the parasite density increases due to higher temperatures.

Figure 3. The amount of parasites per horse where regular and optimized use of anthelmintics is compared. The starting value is 100 000 parasites in the horse. Every time anthelmintics is used there is a sharp decline in the graph. Over a five year period, the regular use of anthelmintics, would be 10 times. For the optimized use, anthelmintics would be used 7 times. The amount of parasites in the horse are lower for the regular use of anthelmintics, but that is understandable, because anthelmintics is used more often. However, in the optimized use, the amount of parasites never exceed an amount which will affect the horse negatively.

Figure 4. The density of parasites per hectare changes where regular and optimized use of anthelmintics are compared. The starting value of parasites in the horse are set to 100 000. The data fluctuates because the temperature changes day to day, which affects the development of an egg turning into a larvae. This can also be seen during the summer months, where the parasite density increases due to higher temperatures.

The model shows that with an optimized use of anthelmintics, no anthelmintics cures would have to be used. In comparison to when the anthelmintics is used regularly, which means that anthelmintics would be used 10 times during a 5 year period. In the calculations where the starting value of parasites in the horse is at 100 000, there would be 3 cures less in the optimized method compared to the regular method. The anthelmintics resistance in parasites increases with the use of anthelmintics, which can be unnecessary in some cases. Which also can be seen in this model.

However, this model doesn’t take into account the encysted larva in the mucosa. This is due to lack of information about when the larva choose to encyst, and when it decides to burst to from the cyst. The communication between the adult parasites and the encysted larva is still a mystery that has to be solved to be able to form an even more accurate model.

Although there’s some shortcomings, the model clearly shows that using anthelmintics only when are needed would decrease the usage of the anthelmintics, and in the long run restrain the growing resistance against different anthelmintics in the parasites.

Survey Modeling

When we had chosen this year's iGEM project, we wanted to investigate how a potential bacteria based product could be integrated in the community. Therefore a survey was conducted and sent out to horseowners all over Europe. Based on the answers we would get more insight into people's awareness of the large and small strongyle, and everything related to them. The marketing analysis was done in collaboration with the human practice part of the project, where human practices worked with which questions would be added into the survey, and the modeling group worked with creating a program that would be used to analyze the results.

In the modeling part of the project, we have created an analyzing program to interpret the answers we received from the survey. The purpose of the analysis was to look for correlations between different variables, for example; is there any correlation between how concerned people are about resistance to strongyle and if they are using any preventive treatments against strongyles?

The information acquired from the model could be used to, for example, investigate how knowledge about anthelmintic resistance could be disseminated in a efficacious manner. Additionally, we wanted to find a potential target market and get an idea of how a potential product could be marketed.

Design

In order to turn the results from the survey into usable data, we first needed to transform all the answers that were in text form to numerical form, and filter out incomplete values, as well. This was done to be able to analyse it further. The survey consisted of several questions that gave answers as discrete data. If we instead, had worked with continuous data, a regression analysis could have been performed [10]. Now, when using discrete data, we needed to find a suitable way to handle this. We chose to use a type of discrete scatter plot with valued points and with histograms [11]. In the discrete scatter plots, the size of the points increases every time a coupling occurs, see an example of a plot in figure 5. In this case, a coupling refers to when a x and a y value exist together. In this way the importance of a couple can easily be visualized. To suspect a correlation, the largest sized points should appear in some kind of linear, exponential or other interesting pattern.

Result

Results that we found interesting are further described on human practices page. To download the model written in R, click here. Figure 5 shows a descriptive discrete scatter plot with valued points and figure 6 shows an application of the latter plot based on real survey data.