Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity

Christinah Chiyaka, Zindoga Mukandavire, Prasenjit Das, Farai Nyabadza, Senelani D Hove-Musekwa, Henry Mwambi

Research output: Contribution to journalArticle

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Abstract

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

Original languageEnglish
Pages (from-to)169-178
Number of pages10
JournalJournal of Theoretical Biology
Volume263
Issue number2
DOIs
Publication statusPublished - 21 Mar 2010

Fingerprint

Plasmodium malariae
cross immunity
Reproductive Isolation
Malaria
Plasmodium falciparum
Immunity
Infection
Theoretical Analysis
Reproductive number
Partial
Aptitude
infection
reproductive isolation
Population
Isolation
competitive exclusion
Interior
qualitative analysis
Model
human population

Keywords

  • Animals
  • Cross Reactions
  • Malaria
  • Models, Theoretical
  • Plasmodium falciparum
  • Plasmodium malariae
  • Journal Article

Cite this

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity. / Chiyaka, Christinah; Mukandavire, Zindoga; Das, Prasenjit; Nyabadza, Farai; Hove-Musekwa, Senelani D; Mwambi, Henry.

In: Journal of Theoretical Biology, Vol. 263, No. 2, 21.03.2010, p. 169-178.

Research output: Contribution to journalArticle

Chiyaka, Christinah ; Mukandavire, Zindoga ; Das, Prasenjit ; Nyabadza, Farai ; Hove-Musekwa, Senelani D ; Mwambi, Henry. / Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity. In: Journal of Theoretical Biology. 2010 ; Vol. 263, No. 2. pp. 169-178.
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AU - Hove-Musekwa, Senelani D

AU - Mwambi, Henry

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N2 - A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.

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