A periodic Ross-Macdonald model in a patchy environment

Daozhou Gao; Yijun Lou; Shigui Ruan

doi:10.3934/dcdsb.2014.19.3133

A periodic Ross-Macdonald model in a patchy environment

Daozhou Gao, Yijun Lou, Shigui Ruan

Research output: Journal article publication › Journal article › Academic research › peer-review

31 Citations (Scopus)

Abstract

Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number ℛ0 and show that either the disease-free periodic solution is globally asymptotically stable if ℛ0 ≤ 1 or the positive periodic solution is globally asymptotically stable if R0 > 1. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.

Original language	English
Pages (from-to)	3133-3145
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	19
Issue number	10
DOIs	https://doi.org/10.3934/dcdsb.2014.19.3133
Publication status	Published - 1 Dec 2014

Keywords

Basic reproduction number
Malaria
Patch model
Seasonality
Threshold dynamics

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.3934/dcdsb.2014.19.3133

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AB - Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number ℛ0 and show that either the disease-free periodic solution is globally asymptotically stable if ℛ0 ≤ 1 or the positive periodic solution is globally asymptotically stable if R0 > 1. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.

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A periodic Ross-Macdonald model in a patchy environment

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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