Mathematical analysis of an epidemic model with direct and indirect transmission modes and two delays

Abstract In this article, we consider an epidemiological model in which we take into account the effects of direct and indirect transmissions. The first mode occurs through direct contact between infectious and susceptible individuals, and the second one will take place through the shedding of virus particles by infectious individuals and their acquisition by susceptible ones. We also study the effect of latency period and time needed for a susceptible person to become infected by indirect transmission mode. By considering the direct and indirect basic reproduction numbers, we define the basic reproduction number R 0 {R}_{0} of the model, which helps us to analyze the stability of equilibria and bifurcation and determine the most sensitive parameters. In conclusion, some numerical simulations are given to confirm the analytical analysis.