Mathematical Model of Caprine Arthritis Encephalitis Considering the Seasonal Breeding

Abstract

This study was aimed at developing mathematical model of caprine arthritis encephalitis (CAE) and considering effective measures to prevent CAE's infection spread. This model took account of the fluctuation of infection rate due to seasonal breeding. New CAE model was constructed based on the sexually transmitted disease (STD) model. The new model was implemented the new function represented cyclical changes of infection rate to include the changes of the seasonal breeding. And definition equation of basic reproductive numbers (R 0 ) was constructed in reference previous study. In order to consider effective measures to prevent CAE's infection, the spread of CAE's infection was performed simulation.

Caprine Arthritis Encephalitis Virus Disease Modelling Review

“…The models proposed in [30][31][32][33] articles are based on SIR models for AIDS and the only horizontal transmission path included in these models is the sexual transmission. These articles are all of the same study group and the authors justify the modelling of the sexual transmission for CAE saying that "there is a possibility that there is an infection by mating".…”

“…The last epidemiological model in the sexually transmitted diseases class was proposed in [32]. This model (Equation ( 6)) is quite similar to the one depicted in Equation ( 4), but it considers the seasonality of the sexual contacts of the goats with a cyclical sexual contacts rate parameter (c M and c F for male and female subpopulations, respectively).…”

“…These articles [30][31][32][33] also present computational simulations using the proposed models. The main features of these simulations are summarised in the Table 1.…”

“…The main features of these simulations are summarised in the Table 1. In [30,31], the authors used for ODEs numerical simulations both the Euler and the Runge-Kutta iterations methods, while in [32], they used just the Euler method and they do not mentioned which method they used in [33]. In both articles from 2013 they analysed just the endemic scenario, while in the articles from 2014 the authors analysed both the disease-free and the endemic scenarios in their simulations.…”

“…In both articles from 2013 they analysed just the endemic scenario, while in the articles from 2014 the authors analysed both the disease-free and the endemic scenarios in their simulations. Besides that, in [30] the authors considered the seasonality of the births in the simulations and in the [32] they considered the seasonality of the births and of the sexual contacts in the simulations. The parameters values used in the simulations were not justified, with exception of the natural mortality and growth rate, which were based in field knowledge.…”