Often described as the world's most deadly infectious disease, Tuberculosis remains a serious health threat in many parts of the world, especially in the developing countries. One of the social barriers hindering TB patients to seek and complete medical attention is stigmatization. In this study, we incorporated stigmatization on a model published by Feng et al. last 2000. We obtained the basic reproduction number and showed conditions where multiple endemic equilibrium will exist depending on a reinfection threshold. The model predicted a significant increase in the basic reproduction number as the level of stigmatization increases. We used optimal control theory to investigate the effect of controls to combat stigmatization and compare these controls with the usual controls such as improving treatment and minimizing reinfection. Simulations show that although stigmatization controls are helpful, they are not enough to successfully control the disease. A combination of all the controls will be ideal and some optimal rates of doing it over time are given, depending on the perceived cost of implementation.

Reaction-diffusion equations are often used in epidemiological models. In this paper, we generalize the algorithm of Meerschaert and Tadjeran for fractional advection-dispersion flow equations to a coupled system of fractional reaction-diffusion like an equation that arises from vector bourne disease modeling.

In this article we consider a microscopic model for the host-vector disease transmission based on configuration space analysis. We model transmission with a birth-death mechanism in the vector component and mobility in the host component. Our intension is to show that a Vlasov type scaling, which is a mean-field-like scaling of an interacting particle system, leads to the known equations used in epidemiology to model host-vector disease spread on the kinetic level. Configuration space analysis is here a very powerful tool. The concepts of harmonic analysis in this framework are used to derive first the dynamics of correlation functions - giving a hierarchical system of equations comparable to the well known BBGKY hierarchy in Hamiltonian dynamics. A proper Vlasov type scaling guaranties that the resulting Vlasov hierarchy is closed and possesses the property of preservation of chaos. The limiting system of time evolution equations is non-linear and strongly related to the well-known Fisher-KPP equations. A numerical analysis strengthens the analytical results. Moreover, the dynamics of case numbers over time gives qualitatively the solution of a SISUV-ODE system. The microscopic dynamics hence leads to the right behavior in the scaling limit.