Abstract This paper considers a susceptible-infected-susceptible epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is described by the nonlinear transmission mechanism of the form S q I p , where 0 < p ⩽ 1 and q > 0. In Peng et al (SIAM J. Math. Anal. (arXiv:2411.00582)), we have studied a model with a constant total population. In the current paper, we extend our analysis to a model with a varying total population, incorporating birth and death rates. We investigate the asymptotic profiles of the endemic equilibrium when the dispersal rates of susceptible and/or infected individuals are small. Our work is motivated by disease control strategies that limit population movement. To illustrate the main findings, we conduct numerical simulations and provide a discussion of the theoretical results from the view of disease control. We will also compare the results for the models with constant or varying total population.