Lie Symmetries and Solutions for a Reaction–Diffusion–Advection SIS Model with Demographic Effects

A reaction–diffusion susceptible–infectious–susceptible disease model with advection, vital dynamics (birth–death effects), and a standard incidence infection mechanism is carefully analyzed. Two distinct diffusion coefficients for the susceptible and infected populations are considered. The Lie symmetries and closed-form solutions for the RDA–SIS disease model are established. The derived solution allows to study dynamics of disease transmission. Our simulation clearly illustrates the evolution dynamics of the model by using the values of parameters from academic sources. A sensitivity analysis is performed, offering valuable perspectives that could inform future disease management policies.