NONLINEAR DYNAMICS AND SIMULATION OF INFECTIOUS DISEASES IN HUMANS

Abstract

Infectious diseases impose a critical challenge to humans and remain to be a matter of global concern. Sometimes contagious diseases that had become rare or had been only local suddenly start occurring worldwide, for instance, SARS, Ebola, and Zika fever. The last two decades have seen several large-scale epidemics outbreaks such as Ebola, SARS, Zika virus, and swine u, which leads to low socioeconomic status and inadequate access to health care. The mathematical modeling of infectious diseases has become a vital tool to understand, predict and control the spread of contagious diseases.

The present thesis aims to discuss the various aspects of transmission dynamics of in- fectious diseases through time-delayed mathematical epidemic models. The inclusion of

time delay in the study of epidemiology is an important aspect. Persons with asymp- tomatic infections play an essential role in spreading infectious diseases, especially as

they are unaware of their illness and take no special hygiene precautions. Thus, the

study of disease-transmission dynamics involves time delay, which needs to be consid- ered for practical purposes. The time delay may arise due to delays caused by the

latency in a vector and delay caused by a latent period in the host. Therefore, this the- sis comprises the Delay-dierential equations for formulating the epidemic models. We

have proposed time-delayed epidemic models with dierent compartments and analyzed them mathematically for positiveness, boundedness, and stability to provide the control strategies of emerging or re-emerging infectious diseases. The mathematical analysis and simulations of the proposed models have been done using the Routh-Hurwitz stability criterion, Descartes' rule of signs, Lyapunov direct method, and Mathematica 11.