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| Mathematical Modelling and Analysis of the Effect of Vaccination and Age Structure on the Transmission and Persistence of Malaria |
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| KeyWord:Malaria, vaccine, environmental factors, health education, non-autonomous ODE |
| Author Name | Affiliation | | S. Djaou\'e | The Faculty of Sciences, University of Maroua, Cameroon | | E. Dangb\'e | LASE-lab, The University Institute of Technology, University of Ngaoundere, Cameroon | | A. Batour\'e Bamana | LASE-lab, The University Institute of Technology, University of Ngaoundere, Cameroon | | Ir\'epran Damakoa | The Faculty of Sciences, University of Ngaoundere, Cameroon | | A. Perasso | UMR6249 Chrono-environment Laboratory, University of Franche-Comt\'e, France |
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| Abstract: |
| Malaria is a vector-borne parasitic disease caused by Plasmodium parasites. It represents the most widespread and lethal parasitic disease globally, with sub-Saharan Africa accounting for over $90\%$ of the reported cases and deaths. Children under five and pregnant women are the most vulnerable to severe malaria infection. To improve malaria control and work towards its eradication, multiple strategies are deployed. These include health education promoting the use of insecticide-treated nets and environmental management, alongside biomedical interventions. Notably, the World Health Organization (WHO) has recommended a malaria vaccine for children aged 0-59 months in high-transmission areas, with an estimated efficacy of $75\%$. Furthermore, the life cycle of the mosquito vector, and thus disease transmission, is strongly influenced by climatic factors such as temperature and rainfall. Consequently, these factors must be integrated into models analysing transmission dynamics. This paper evaluates the combined impact of vaccination, health education, and climatic factors to identify optimal malaria control strategies. We propose a mathematical model described by a system of differential equations, subdividing the population into two main age groups: children under five years and individuals aged five years and over. A subclass of vaccinated children is included within the younger age group. We establish the basic properties guaranteeing the model's biological feasibility, derive the basic reproduction number ($\mathcal{R}_0$), and analyse the model's asymptotic behaviour. Numerical simulations are performed to verify the analytical results. Using climate data from two Cameroonian cities with distinct profiles, Maroua and Ngaoundere, our simulations indicate that malaria transmission can be controlled if at least $70\%$ of the population is reached by health education initiatives. In the case where $50\%$ of children under five years is vaccinated, this required coverage for health education reduces to $55\%$ to achieve control. |
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