Mathematical model of malaria with seasonal evolution of mosquitoes population: case of Burkina Faso

Document Type : Regular research papers

Authors

1 Departement de Mathématique, Université Nazi Boni, Bobo Dioulasso, Burkina Faso

2 Université virtuelle du Sénégal, Dakar, Sénégal.

Abstract

This work is devoted to the formulation and study of mathematical
model of malaria transmission taking into account the seasonal evolution of the
vector populations.The aim is to examine the impact of the seasonal variation
of mosquitoes on the
uctuation of malaria cases in Burkina Faso. The human
population is divide to susceptible (Sh), exposed (Eh), infected (Ih) and recovered
(Rh). The vector population is divided to susceptible (Sv) and infected
(Iv). The basic mathematical properties of the model such as the boundedness
and positivity of the solutions are established. The basic reproduction number
R0 of the model is determined. The global stability of the endemic and disease
free equilibrium point is proven. The impact of seasonality and temperature on
vector dynamics (the function f) is developed to determine the intense period
of mosquitoes. The sensitivity of the parameters is studied to determine the
most sensitive parameters in the evolution of the malaria disease. We use the
Python software for the numerical simulation of the model. The real data on
the number of malaria cases in Burkina Faso is used in the simulation section to
illustrate the mathematical analysis. This study highlights that an increase in
the mosquito population leads to a rise in malaria cases, while their reduction
results in a decrease in cases. It also shows that the month with a high incidence
of malaria in BURKINA Faso are July, August, September and October,
whereas the months with fewer cases are July and February.

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History

  • Receive Date: 25 May 2024
  • Revise Date: 23 September 2024
  • Accept Date: 18 November 2024

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