Mathematical and computational models for the spread of tick-borne diseases on host populations

Abstract

The importance of population modeling has driven many researchers and scientists to study mathematical models that analyze and observe the dynamics of a certain population. This field is very wide and includes many topics such as infectious diseases. Many models for the spread of infectious diseases in populations have been mathematically analyzed and applied to specific diseases. The wide spread of viruses, bacteria and infectious ticks draw the attention to analyze, predict and even control diseases caused by them. Mathematical models, computational implementations and statistical data analysis are main tools which help humans control these diseases. Our main target in this thesis is to be able to understand the dynamics of interaction between an infected tick-vector invading a certain host population (mostly bovines, horses, …). This leads to the ability to predict the status of the host population in the future time and thus prevent any case of an epidemic. We will be using an SIR model which governs this above mentioned tick-host interaction. We will study this model and analyze it before we implement it. After that we will perform Maximum Likelihood Estimations on some important rates in the model which will help us determine whether the population under study is at a risk of an epidemic or not. In order to do this, we had to use field data for two horse populations from two regions in Rio de Janeiro (Brazil, 2011). In these two regions researchers have found a very high percentage of infection among horses. After we have implemented our model and used it in estimating the infection rate and recovery rate of the population in those regions, we were able to calculate a threshold value which predicted an epidemic. Doing this, we have found a way to predict any kind of disease threats facing any population even human beings.