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A Malaria Transmission Model with Temperature-Dependent Incubation Period

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Abstract

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio \(R_0\) and establish a threshold type result on the global dynamics in terms of \(R_0\), that is, the unique disease-free periodic solution is globally asymptotically stable if \(R_0<1\); and the model system admits a unique positive periodic solution which is globally asymptotically stable if \(R_0>1\). Numerically, we parameterize the model with data from Maputo Province, Mozambique, and simulate the long-term behavior of solutions. The simulation result is consistent with the obtained analytic result. In addition, we find that using the time-averaged EIP may underestimate the basic reproduction ratio.

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Acknowledgements

We are very grateful to two anonymous referees for their careful reading and helpful suggestions which led to an important improvement of our original manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada

    Xiunan Wang & Xiao-Qiang Zhao

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  1. Xiunan Wang
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  2. Xiao-Qiang Zhao
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Correspondence to Xiunan Wang.

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This work is supported in part by the NSERC of Canada.

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Wang, X., Zhao, XQ. A Malaria Transmission Model with Temperature-Dependent Incubation Period. Bull Math Biol 79, 1155–1182 (2017). https://doi.org/10.1007/s11538-017-0276-3

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  • DOI: https://doi.org/10.1007/s11538-017-0276-3

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