Mathematical analysis of a stochastic tuberculosis model

Abstract

The main objective of this work is to include randomness into the model for dynamics of tuberculosis. Stochasticity to the model is introduced through perturbation of parameters which is a standard method in stochastic population modeling. The well-posedness analysis of SDEs includes the existence of non-negative solutions as required in the dynamics of population modeling. A detailed stability analysis of results, analytical properties and asymptotical behavior of solutions is also done. The mean reverting process is approximated for one of the variables and the mean and variance of the process are found.