Abstract
This paper deals with a reaction-diffusion model on a periodically and isotropically evolving domain in order to explore the diffusive dynamics of Aedes aegypti mosquito, where we divide it into two sub-populations: the winged population and an aquatic form. The spatial-temporal risk index $ R_0(\rho) $ depending on the domain evolution rate $ \rho(t) $ as well as its analytical properties is investigated. The long-time behaviors of the periodic solutions under the condition $ R_0(\rho)>1 $ and $ R_0(\rho)\leq1 $ are explored, respectively. Moreover, we consider the specific case where $ \rho(t)\equiv1 $ to better understand the impact of the periodic evolution rate on the persistence and extinction of Aedes aegypti mosquito. Numerical simulations further verify our analytical results that the periodic domain evolution has a significant impact on the dispersal of Aedes aegypti mosquito.
Highlights
Infectious diseases caused by insect vectors such as mosquitoes have been a considerable threat to human health
We first carry out numerical simulations on R1 space to illustrate the theoretical results
The result is in accordance with Theorem 3.3 that the mosquitoes with periodically evolving domain will persist, which means that the evolution rate ρ(t) with ρ−2 < 1 has a positive effect on the persistent of Aedes aegypti mosquito
Summary
Infectious diseases caused by insect vectors such as mosquitoes have been a considerable threat to human health. Reaction-diffusion model, Aedes aegypti mosquito, periodically evolving domain, spatial-temporal risk index, long-time behavior. The oviposition rate, maturation rate as well as the mortality rates of the Aedes aegypti mosquito will change with seasonal fluctuation, so does their living habitat Female mosquitoes lay their eggs in small containers that hold water, which are relevant to the humidity, rainfall, maybe as well as the rivers nearby. The basic reproduction number could be expressed in the term of the principal eigenvalues of relevant eigenvalue problems, similar results to Lemma 2.1 can be seen in [2, 35] for reaction-diffusion problem and in [21, 37] for periodic-parabolic problems. (2.11) is equivalent to p(t) p(t) q(t) p(t) μ1(t) +
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