Mathematical simulation of contagious virus spread

In this article we study the prevalence of contagious disease in a community. To this end, we view society as a dynamic system and apply mathematical equations and relationships to it. First, we present the history of mathematical modeling in the field of contagious diseases and the work done in this field, then find out the probability of the virus spreading in a population with a number of people with contagious disease, and finally the differential equation of disease spread. Obtain the environment and then calculate the time it took to get the disease. In addition, we also plan to provide a model to describe how a virus is transmitted. In this model, we have four boxes called susceptible individuals, virus carriers, treated individuals, and improved individuals. We obtain the differential equations of growth and decline of each of these boxes and examine the stability condition of the system.