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]

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.

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