Mathematical optimization modeling for estimating the incidence of clinical diseases

The notion that infectious disease transmission and dissemination are governed by rules that may be expressed mathematically is not new. In fact, the nonlinear dynamics of infectious illness transmission were only fully recognized in the twentieth century. However, with the Coronavirus outbreak, there is a lot of discussion and study regarding the origin of the epidemic and how it spreads before all vulnerable people are infected, as well as ideas about how the disease virulence changes during the epidemic. In this paper, we provide some critical mathematical models which are SIR and SIS and their differences in approach for the interpretation and transmission of viruses and other epidemics as well as formulate the optimal control problem with vaccinations.