A mathematical model for malaria disease dynamics with vaccination and infected immigrants

Pride Duve; Samuel Charles; Justin Munyakazi; Renke Lühken; Peter Witbooi; Pride Duve; Samuel Charles; Justin Munyakazi; Renke Lühken; Peter Witbooi

doi:10.3934/mbe.2024045

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1082-1109. doi: 10.3934/mbe.2024045

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A mathematical model for malaria disease dynamics with vaccination and infected immigrants

1.
African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg, Cape Town, Republic of South Africa
2.
Bernhard-Nocht Institute for Tropical Medicine, Bernhard-Nocht Straße, 74, Hamburg, Germany
3.
Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, Republic of South Africa
4.
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK

Academic Editor: Higinio Ramos

Received: 08 September 2023 Revised: 29 November 2023 Accepted: 11 December 2023 Published: 22 December 2023

The world is aiming to eliminate malaria by 2030. The introduction of the pilot project on malaria vaccination for children in Kenya, Ghana, and Malawi presents a significant thrust to the elimination efforts. In this work, a susceptible, infectious and recovered (SIR) human-vector interaction mathematical model for malaria was formulated. The model was extended to include a compartment of vaccinated humans and an influx of infected immigrants. Qualitative and quantitative analysis was performed on the model. When there was no influx of infected immigrants, the model had a disease-free equilibrium point that was globally asymptotically stable when a threshold known as the basic reproductive number denoted by $ R_0 $ was less than one. When there was an influx of infected immigrants, the model had endemic equilibrium points only. Parameter sensitivity analysis on $ R_0 $ was performed and results showed that strategies must be implemented to reduce contact between mosquitoes and humans. Results from different vaccine coverage indicated that in the absence of an influx of infected immigrants, it is possible to achieve a malaria-free society when more children get vaccinated and the influx of infected humans is avoided. The analysis of the optimal control model showed that the combined use of vaccination, personal protective equipment, and treatment is the best way to curb malaria incidence, provided the influx of infected humans is completely stopped.
- vaccination,
- immigration,
- optimal control,
- reproductive number,
- equilibrium points
Citation: Pride Duve, Samuel Charles, Justin Munyakazi, Renke Lühken, Peter Witbooi. A mathematical model for malaria disease dynamics with vaccination and infected immigrants[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1082-1109. doi: 10.3934/mbe.2024045

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Abstract

The world is aiming to eliminate malaria by 2030. The introduction of the pilot project on malaria vaccination for children in Kenya, Ghana, and Malawi presents a significant thrust to the elimination efforts. In this work, a susceptible, infectious and recovered (SIR) human-vector interaction mathematical model for malaria was formulated. The model was extended to include a compartment of vaccinated humans and an influx of infected immigrants. Qualitative and quantitative analysis was performed on the model. When there was no influx of infected immigrants, the model had a disease-free equilibrium point that was globally asymptotically stable when a threshold known as the basic reproductive number denoted by $ R_0 $ was less than one. When there was an influx of infected immigrants, the model had endemic equilibrium points only. Parameter sensitivity analysis on $ R_0 $ was performed and results showed that strategies must be implemented to reduce contact between mosquitoes and humans. Results from different vaccine coverage indicated that in the absence of an influx of infected immigrants, it is possible to achieve a malaria-free society when more children get vaccinated and the influx of infected humans is avoided. The analysis of the optimal control model showed that the combined use of vaccination, personal protective equipment, and treatment is the best way to curb malaria incidence, provided the influx of infected humans is completely stopped.

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