The Spread Pattern of COVID-19 Disease Using Stochastic Differential Equation Susceptible Infected Susceptible Model

Abstract

Epidemic is the major transmission of an infectious disease that spreads quickly in a large area and causes many victims. Epidemic model is one of the tools that can be used to study the pattern of disease outspread. The SIS model describes the transmission of disease from an individual who is susceptible then infected, directly or indirectly, and becomes an infected individual. Individuals who have been infected can recover but remain susceptible to re-infection because they do not have permanent immunity. COVID-19 is an infectious disease caused by the SARS-CoV-2 virus, an individual can be infected with this disease by breathing air that containing the virus if they are standing close proximity with individuals who are already infected with COVID-19. The purpose of this study was to see the pattern of transmission of infectious diseases using SDE SIS through model simulation and provide interpretation. In this study, rate of contact affected the duration of infectious diseases outspread. The study was conducted by applying a model simulation, given the parameter values of  (percentage of the population who recovered each period) and  (probability of infection contact between infected individuals and susceptible individuals). The simulation results for the values of  and  show that the graph of the number of infected individuals increases sharply and tends to be constant at . The number of infected does not decrease again due to the characteristics of the SIS epidemis model, where individuals who recover do not have permanent immunity to the disease, so that the individual becomes susceptible to the disease again.