Analysis of an epidemic spreading model with exponential decay law

Abstract

Mathematical modeling of infectious diseases has shown that combinations of isolation, quarantine,vaccine, and treatment are often necessary in order to eliminate most infectious diseases. Continuousmathematical models have been used to study the dynamics of infectious diseases within a humanhost and in the population. We have used in this study a SIR model that categorizes individuals in apopulation as susceptible (S), infected (I) and recovered (R). It also simulates the transmission dynamicsof diseases where individuals acquire permanent immunity. We have considered the SIR model using theCaputo-Fabrizio and we have obtained special solutions and numerical simulations using an iterativescheme with Laplace transform. Moreover, we have studied the uniqueness and existence of the solutions.