Dynamics of a multi-strain malaria model with diffusion in a periodic environment

Abstract

This paper mainly explores the complex impacts of spatial heterogeneity, vector-bias effect, multiple strains, temperature-dependent extrinsic incubation period (EIP) and seasonality on malaria transmission. We propose a multi-strain malaria transmission model with diffusion and periodic delays and define the reproduction numbers [Formula: see text] and [Formula: see text] (i = 1, 2). Quantitative analysis indicates that the disease-free ω-periodic solution is globally attractive when [Formula: see text], while if [Formula: see text] ([Formula: see text]), then strain i persists and strain j dies out. More interestingly, when [Formula: see text] and [Formula: see text] are greater than 1, the competitive exclusion of the two strains also occurs. Additionally, in a heterogeneous environment, the coexistence conditions of the two strains are [Formula: see text] and [Formula: see text]. Numerical simulations verify the analytical results and reveal that ignoring vector-bias effect or seasonality when studying malaria transmission will underestimate the risk of disease transmission.

Keywords

• Vector-bias malaria model
• multi-strain
• heterogeneity
• reproduction number
• periodic solution