Mathematical modelling of the interactive dynamics of wild and <i>Microsporidia MB</i>-infected mosquitoes

Charlène N. T. Mfangnia; Henri E. Z. Tonnang; Berge Tsanou; Jeremy Herren; Charlène N. T. Mfangnia; Henri E. Z. Tonnang; Berge Tsanou; Jeremy Herren

doi:10.3934/mbe.2023679

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 15167-15200. doi: 10.3934/mbe.2023679

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Mathematical modelling of the interactive dynamics of wild and Microsporidia MB-infected mosquitoes

1.
Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box: 67, Cameroon
2.
International Centre of Insect Physiology and Ecology (icipe), Nairobi, P.O. Box: 30772, Kenya
3.
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Academic Editor: Sanling Yuan

Received: 06 April 2023 Revised: 17 June 2023 Accepted: 26 June 2023 Published: 18 July 2023

A recent discovery highlighted that mosquitoes infected with Microsporidia MB are unable to transmit the Plasmodium to humans. Microsporidia MB is a symbiont transmitted vertically and horizontally in the mosquito population, and these transmission routes are known to favor the persistence of the parasite in the mosquito population. Despite the dual transmission, data from field experiments reveal a low prevalence of MB-infected mosquitoes in nature. This study proposes a compartmental model to understand the prevalence of MB-infected mosquitoes. The dynamic of the model is obtained through the computation of the basic reproduction number and the analysis of the stability of the MB-free and coexistence equilibria. The model shows that, in spite of the high vertical transmission efficiency of Microsporidia MB, there can still be a low prevalence of MB-infected mosquitoes. Numerical analysis of the model shows that male-to-female horizontal transmission contributes more than female-to-male horizontal transmission to the spread of MB-infected mosquitoes. Moreover, the female-to-male horizontal transmission contributes to the spread of the symbiont only if there are multiple mating occurrences for male mosquitoes. Furthermore, when fixing the efficiencies of vertical transmission, the parameters having the greater influence on the ratio of MB-positive to wild mosquitoes are identified. In addition, by assuming a similar impact of the temperature on wild and MB-infected mosquitoes, our model shows the seasonal fluctuation of MB-infected mosquitoes. This study serves as a reference for further studies, on the release strategies of MB-infected mosquitoes, to avoid overestimating the MB-infection spread.
- Microsporidia MB,
- Plasmodium transmission-blocking,
- vertical-horizontal transmission,
- compartmental modelling,
- seasonality,
- malaria bio-control
Citation: Charlène N. T. Mfangnia, Henri E. Z. Tonnang, Berge Tsanou, Jeremy Herren. Mathematical modelling of the interactive dynamics of wild and Microsporidia MB-infected mosquitoes[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 15167-15200. doi: 10.3934/mbe.2023679

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Abstract

A recent discovery highlighted that mosquitoes infected with Microsporidia MB are unable to transmit the Plasmodium to humans. Microsporidia MB is a symbiont transmitted vertically and horizontally in the mosquito population, and these transmission routes are known to favor the persistence of the parasite in the mosquito population. Despite the dual transmission, data from field experiments reveal a low prevalence of MB-infected mosquitoes in nature. This study proposes a compartmental model to understand the prevalence of MB-infected mosquitoes. The dynamic of the model is obtained through the computation of the basic reproduction number and the analysis of the stability of the MB-free and coexistence equilibria. The model shows that, in spite of the high vertical transmission efficiency of Microsporidia MB, there can still be a low prevalence of MB-infected mosquitoes. Numerical analysis of the model shows that male-to-female horizontal transmission contributes more than female-to-male horizontal transmission to the spread of MB-infected mosquitoes. Moreover, the female-to-male horizontal transmission contributes to the spread of the symbiont only if there are multiple mating occurrences for male mosquitoes. Furthermore, when fixing the efficiencies of vertical transmission, the parameters having the greater influence on the ratio of MB-positive to wild mosquitoes are identified. In addition, by assuming a similar impact of the temperature on wild and MB-infected mosquitoes, our model shows the seasonal fluctuation of MB-infected mosquitoes. This study serves as a reference for further studies, on the release strategies of MB-infected mosquitoes, to avoid overestimating the MB-infection spread.

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