Asymptotic dynamics and optimal control of a reaction-diffusion yellow fever model in a heterogeneous environment

A reaction-diffusion model for yellow fever (YF) combining pesticides, education, vaccination, treatment, standard incidence rate, distinct dispersal rates and spatial heterogeneity is constructed. The joint consideration of comprehensive measures, distinct dispersal rates and spatial heterogeneity poses challenges in exploring the transmission and control strategy of YF. The basic reproduction number R0 is introduced to determine whether the infection will persist. Moreover, the asymptotic profiles of R0 in the case of small or large dispersal rates are disclosed by overcoming the difficulties caused by the 4 different non-constant dispersal rates. Further, the existence of optimal control and the necessary optimality condition of the optimal control problem in a spatially heterogeneous environment is investigated by semigroup theory and the minimizing sequence technique. We take the BP neural network method to estimate the parameters based on the accumulated cases of YF in Luanda, Angola. Numerical simulations are performed to reveal the impacts of dispersal rates, spatial heterogeneity, control measures and the two forms of control on the prevalence intensity of YF. More importantly, the 16 different control strategies have been quantified by calculating four indexes, highlighting the most effective strategy and the most cost-effective strategy.