The Closed-Form Solutions of an SIS Epidemic Reaction–Diffusion Model with Advection in a One-Dimensional Space Domain

This work investigates a class of susceptible–infected–susceptible (SIS) epidemic model with reaction–diffusion–advection (RDA) by utilizing the Lie group methods. The Lie symmetries are computed for the three widely used incidence functions: standard incidence, mass action incidence, and saturated incidence. The Lie algebra for the SIS-RDA epidemic model is four-dimensional for the standard incidence function, three-dimensional for mass action incidence, and two-dimensional for saturated incidence. The reductions and closed-form solutions for the SIS-RDA epidemic model for the standard incidence infection mechanism are established. The transmission dynamics of an infectious disease utilizing closed-form solutions is presented. To illustrate the paths of susceptible and infected populations, we consider the Cauchy problem. Moreover, a sensitivity analysis is conducted to provide insights into potential policy recommendations for disease control.