Mathematical analysis of a malaria model with partial immunity to reinfection
type: Item
instance of: scholarly article
title: Mathematical analysis of a malaria model with partial immunity to reinfection
zbMATH Open document ID: 1284.37060
DOI: 10.1155/2013/405258
author: Abid Ali Lashari
author: Il Hyo Jung
author: Kazeem Oare Okosun
author: Young Il Seo
author: Liming Cai
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: In this paper, a deterministic model with variable human population for the transmission dynamics of malaria disease, which allows transmission by the recovered humans, is first developed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where the stable disease-free equilibrium coexists with a stable endemic equilibrium. This phenomenon may arise due to the reinfection of host individuals who recovered from the disease. The model in an asymptotically constant population is also investigated. A complete global analysis of the model with mass action incidence is given, which reveals that the global dynamics of the malaria disease with reinfection is completely determined by the associated reproduction number. Moreover, it is shown that the phenomenon of backward bifurcation can be removed by replacing the standard incidence function with a mass action incidence. Graphical representations are provided to study the effect of the reinfection rate and to qualitatively support the analytical results on the transmission dynamics of the malaria.
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 6161328
zbMATH Keywords: malaria model
zbMATH Keywords: partial immunity
zbMATH Keywords: backward bifurcation
reviewed by: Xueyong Zhou
MaRDI profile type: Publication
Wikidata QID: Q57620370
full work available at URL: https://doi.org/10.1155/2013/405258
OpenAlex ID: W2035034119
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description: scientific article; zbMATH DE number 6161328