An Almost Periodic Ross-Macdonald Model With Time Delay In A Patchy Environment

Malaria is a vector-borne disease transmitted by the bite of Anopheles mosquitoes.Its transmission and prevalence are affected by many factors.Due to the incubation period of pathogens in humans and mosquitoes and the influence of human activities between cities and villages,time delay and population spread play a very important role in the spread of diseases.In addition,the inhomogeneity of time is also an important factor.It is generally caused by seasonal factors and is reflected by the periodicity of time.As generalization of periodic functions,almost periodic functions can reveal more comprehensively the influence of seasonality.First,this paper uses the concept of”age of infection” to derive the almost periodic Ross-Macdonald model with time delay in the patch environment.Secondly,it proves the existence of disease-free almost periodic solutions of this model and defines the basic regeneration ratio R₀ by the next generation of operators.And then we prove that R₀ is a threshold result,that is,when R₀>1,the model exacts a positive almost periodic solution,and the disease is uniformly persistent,When R₀<1,and the number of patients in the initial stage of infection is small,or the susceptible,latent,and infected have the same migration rate between different patches,the disease will die.Finally,numerical simulations were carried out for the almost periodic malaria models on the two patches,and the numerical simulation results were consistent with the theoretical results.At the same time,the periodic model is compared with the almost periodic model.If the almost periodic model is replaced by the periodic model,the value of R₀ will be underestimated or overestimated.