Anthelmintic Resistance Model

Design

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 time 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 amount of horses, the temperature dependence of the parasite egg to develop into a larva and the amount of 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 an ordinary differential equation (equation 1). 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]

Variables	Value	Description
L		Density of infective larvae
A		Mean number of adult parasites per horse
ρ	0.025[4]	Rate at which larva is lost from pasture, with other reasons than being eaten by the horses
β(A)	6 or 20	Rate at which larvae are eaten by a single horse. Regular rate is 20, if adult worms exceeds 100 000 the food intake reduces by 70% to 6.
H	1	Horse population density per ha
q(T)	Equation 2	Probability that an egg develops into an larvae, which is temperature, T (C), dependent
λ	54 [4]	Mean rate at which an adult worm produces eggs
d	XXXXX [4]	The probability that an ingested larva develops into an adult worm
μ	XXXXXXXX [4]	Mortality rate of adult parasites
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 are temperature dependent, an 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 an 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. Therefore the constants in the equation was divided with 20 to match it. The temperature data was used was from the Uppsala weather stations measurement during 2017. (referens SMHI)

Beta is the amount of square meters grass a horse eats per day, a horse eats approximately five times more than a sheep. [7][8] Beta decreases if the amount of parasites in the gastrointestinal area of the horse exceeds an amount that is non-detrimental to the horses 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 my, mortality rate of adult parasites, lambda, 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, and only varying when anthelmintics are 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 L_0, the density of worms per ha pasture, is 1000, and A_0 is either 10000 and 0. The results of the calculations are shown in the graphs.

Survey modeling

Introduction

When we had chosen this years iGEM project, we wanted to investigate how a potential bacteria based product could be integrated in the community and therefore a survey was conducted and sent out to people in the horse field. 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.

In the modeling part of the project, we have created a model to interpret the answers we received from the survey. The purpose of the model is to look for correlation 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 knowledge acquired from the model could be used to, for example, investigate how knowledge about anthelmintic resistance could be disseminated in a efficacious manner. Also, to find a potential target market and to give 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 [9]. 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 [10]. Every time a coupling occurs the size of the points will increase, see an example of a plot in figure 1. 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

To download the model written in R, click here. Figure 1 shows a descriptive discrete scatter plot with valued points and figure 2 shows an application of the latter plot based on real survey data.

Figure 1. Descriptive discrete scatter plot with valued points. The numbers in the points describes the number of couplings.

Figure 2. An example of an discrete scatter plot with valued points based on data from the survey.

1. Traversa D, Klei TR, Iorio R, Paoletti B, Lia RP, Otranto D, et al. Occurrence of anthelmintic resistant equine cyathostome populations in central and southern Italy. Prev Vet Med. 2007;82: 314–320.

2. Lind EO, Kuzmina T, Uggla A, Waller PJ, Höglund J. A field study on the effect of some anthelmintics on cyathostomins of horses in sweden. Vet Res Commun. 2007;31: 53–65.

3. Lind EO, Rautalinko E, Uggla A, Waller PJ, Morrison DA, Höglund J. Parasite control practices on Swedish horse farms. Acta Vet Scand. 2007;49: 25.

4. Pech CL, Doole GJ, Pluske JM. Economic management of anthelmintic resistance: model and application. Aust J Agric Resour Econ. 2009;53: 585–602.

5. Karlsson J. Parasite detection in extensively hold Gotland ponies. Uppsala: SLU, Institutionen för biomedicin och veterinär folkhälsovetenskap; 2015; 42.

6. Rupasinghe D, Ogbourne CP. Laboratory studies on the effect of temperature on the development of the free-living stages of some strongylid nematodes of the horse. Zeitschrift f�r Parasitenkunde. 1978;55: 249–253.

7. Council NZS. A guide to feed planning for sheep farmers. Beef+ Lamb New Zealand. 2012; 1–55.

8. The Rules of Feeding Your Horse. In: The humane society of United States [Internet]. [cited 12 Oct 2018]. Available: http://www.humanesociety.org/animals/horses/tips/rules_horse_feeding.html

9. Schneider, Astrid, Gerhard Hommel, och Maria Blettner. ”Linear Regression Analysis”. Deutsches Ärzteblatt International107, nr 44 (november 2010): 776–82. https://doi.org/10.3238/arztebl.2010.0776.

10. The R graphs gallery (n.d.). #5 CORRELATION OF DISCRETE VARIABLES, http://www.r-graph-gallery.com/5-correlation-of-discrete-variables/ [2018-10-14]