Averaging Principle for A Stochastic Delayed Avian Influenza Model with Impulsive Perturbations and Fractional Riemann‐Liouville‐Type Contact Rates

ABSTRACT Upon exposure to infectious individuals, susceptible hosts exhibit heterogeneous clinical manifestations ranging from viral carriage without overt symptomatology to progressive symptomatic infection under the effects of the incubation period and external environmental disturbances. Meanwhile, the current rate of change in the number of susceptible hosts is influenced not only by ongoing contact with infected hosts during the incubation period, but also by previous interactions. To characterize the memory and historical cumulative effects of this infection process, this paper formulates a stochastic delayed avian influenza model with impulsive perturbations and fractional Riemann‐Liouville‐type contact rates. The well‐posedness of mild solutions for this model is established using the semigroup method and the Banach fixed‐point theorem. Additionally, an averaging principle is derived by employing inequality techniques and appropriate transformations for the fractional avian influenza model. The theoretical results indicate that the solution of the original impulsive avian influenza system can be effectively approximated by that of a simplified non‐impulsive temporally averaged stochastic system, thereby providing a way to reduce system complexity. Numerical simulations are presented to validate the theoretical results.