Derivation analysis of a discrete-time SIS epidemic model with extension of Markov Chain and logistic map

Abstract

In recent years, the rampant spread of diseases has led to considerable impacts on human society. Limiting such spread requires the formulation of quantitative studies to understand the dynamics of infection and to study the effect of preventative and counteractive action. In 1911, scientists constructed differential equations to study the spread of malaria and found that at a critical mosquito population level the spread of the disease would be limited. This also became the basis for the later dynamics of infectious diseases. This research aims to dynamically analyze the spread of the virus by establishing a mathematical model and assigning specific values to the influencing factors to discuss the relationship between the person who infects others and the infected person. The ultimate goal is that the spread of the disease can be effectively suppressed in a specific proportion of people.

Keywords: dynamics of infectious diseases, infected-uninfected relationship.