This research investigates a qualitative analysis of a reaction–diffusion SIS epidemic model with non-constant recruitment and spatiotemporal heterogeneity. The parameter functions are supposed to be spatially heterogeneous and periodic in time. The global stability of the disease-free \(\omega \) -periodic steady state is shown when \({\mathcal {R}}_0<1\) . Whereas \({\mathcal {R}}_0>1\) , it is obtained that the solution is uniformly persistent, and the model admits at least one positive \(\omega \) -periodic steady state. When the parameter functions are spatially homogeneous, the global stability of this steady state is obtained. Such a result ensures the threshold role of the basic reproduction number \({\mathcal {R}}_0\) . In the case of a spatially heterogeneous environment, we investigated the spatial profile of the positive steady state in both cases and the small and large mobility rates for the susceptible and infected populations. Theoretical findings indicate that a fluctuating total population can increase infectious disease persistence, making the disease more risky and difficult to contain.
