 Threshold and stability results in a periodic model for malaria transmission with partial immunity in humansMahmoud A. Ibrahim and Attila Dénes Applied Mathematics and Computation, 2021, vol. 392, issue C Abstract: We develop a periodic compartmental population model for the spread of malaria, dividing the human population into two classes: non-immune and semi-immune. The effect of seasonal changes in weather on the malaria transmission is considered by applying a non-autonomous model where mosquito birth, death and biting rates are time-dependent. We show that the global dynamics of the system is determined by the basic reproduction number, which we define as the spectral radius of a linear integral operator. For values of the basic reproduction number less than unity, the disease-free periodic solution is globally asymptotically stable, while if R0>1, then the disease remains endemic in the population. We show simulations in accordance with the analytic results. Finally, we show that the time-average reproduction rate gives an underestimation for malaria transmission risk. Keywords: Periodic epidemic model; Malaria transmission; Partial immunity; Basic reproduction number; Global stability; Uniform persistence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306640 DOI: 10.1016/j.amc.2020.125711 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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