Mathematical modeling and analysis with various parameters, for infection dynamics of Tuberculosis

Abstract

Abstract Mathematical model is needed to study the epidemiology of tuberculosis. Here we have proposed a model that is more realistic. We are exhibiting a theoretical framework for getting the control and eradication methodologies to minimize the number of infectious tuberculosis cases in the community. For this purpose, the model population has been compartmentalized and the consequential model equations have been solved analytically. Numerical Simulation has been given to validate the results obtained by the theoretical approach. The effect of latent periods on the epidemics of tuberculosis with respect to population density has been studied. The equilibrium points of the model are calculated and their stability is established by using the ‘Basic Reproduction number’. It is observed that when basic reproduction number is less or equal to unity, the disease-free equilibrium point (DEF) is globally asymptotically stable, while when it is greater to unity, the endemic equilibrium point (EE) is globally asymptotically stable i.e., illness will persist in the population and epidemic will turn out to be endemic. Also, it is obtained that compactness of people decides the infection rate of tuberculosis i.e. the risk of instability of disease free equilibrium increases as the population density increases.