MATHEMATICAL MODELING IN EPIDEMIOLOGY

Abstract

In the present thesis, various aspects of the transmission dynamics of epidemics are discussed through the mathematical models. We have proposed and analyzed the various mathematical models to control the spread of emerging/ re-emerging epidemics. We have investigated the facts and reasons behind the spread and control of infectious diseases/ epidemics. After analyzing several systems, various results obtained by analysis of the problem are discussed. The mathematical models have been analyzed for positiveness, boundedness, and stability. Locals stability, global stability, Routh-Hurwitz stability criterion, Descartes’ rule of signs, Lyapunov function, MATLAB 2012b (ODE 45, DDE 23), MATHEMATICA 11 are the main tools applied for analysis and simulations of mathematical models.

We have studied two types of mathematical models: ordinary differential equations (ODEs) model and delay differential equations (DDEs) model. The time delay exists almost in every biological phenomenon and is responsible for the severity of the disease and hence in its treatment. Therefore, the importance of the DDE model cannot be ignored in the control and transmission dynamics of the epidemic. The DDE models have been developed for a better understanding of the transmission dynamics of epidemics.