Taking into account the influence of climatic factors and age in the mathematical modeling and analysis of the dynamic transmission of malaria
摘要
Malaria is the most widespread and deadly parasitic disease in the world. This disease is transmitted from an infected individual to a healthy individual via the female Anopheles mosquito. Children under the age of 5 are most at risk from this infectious disease. Sub-Saharan Africa is most affected by malaria in the world. The geographical distribution and seasonality of the malaria cases observed are closely related to the climatic factors (temperature and precipitation) that influence its transmission dynamics. To control this disease, the use of insecticide treated nets and education of the population for a clean environment without mosquito breeding grounds has been advocated. To perform a mathematical analysis of malaria dynamics, a mathematical model describing malaria transmission must take into account intra-annual climate variation, compliance with measures to reduce contact with mosquitoes, and the age structure of the population. Some mathematical models developed are mainly concerned with the influence of climatic factors on transmission dynamics. Other models are being developed to assess the impact of control factors such as the use of insecticide-treated nets on the behaviour of changes in the number of malaria cases. For a more appropriate analysis, in this paper, we simultaneously assess the impact of climate, the proportion of people who comply with malaria control measures, and the age structure of the population. To take into account the temporal variation of the defined parameters as a function of temperature and precipitation, we describe the dynamics of malaria transmission using a non-autonomous system of ordinary differential equations. The mathematical analysis of the model allowed us to establish the biological properties and asymptotic behavior of the model solutions. From numerical simulations, we assessed the threshold proportion of people who comply with the rules that is necessary to control malaria dynamics, which is 0.5. Using two cities in Cameroon, Maroua and Ngaoundere with different climatic data, we highlighted the influence of climate on the evolution of the number of new malaria cases.