Mathematical Study of Malaria Transmission Dynamics with Treatment

Abstract

Malaria is a vector-borne infectious disease transmitted to humans by the bite of female Anopheles mosquitoes. A compartmental model is proposed to study the transmission dynamics of the disease, treating humans as hosts and mosquitoes as vectors. This work focuses on the treatment of infected humans, which plays a crucial role in controlling the transmission dynamics of malaria. It is a key factor to understand disease dynamics which helps in guiding the public health polices decisions to ensure the effective disease control strategies. The human population is divided into the five compartments, namely Susceptible, Exposed, Infectious, Treatment and Recovered and the mosquito population is divided into three compartments such as Susceptible, Exposed and Infectious. The dynamics of malaria transmission are represented through compartmental models and formulated as ordinary differential equations. We prove the positivity and boundedness properties of the model equations to ensure the well-posedness of both the population dynamics. The dimensionless quantity known as the basic reproduction number R₀ , which determines whether the disease dies out or persists in the population, is calculated using the method of the next generation matrix. It is observed that the disease-free equilibrium point is stable, leading to the disease extinction, when R₀ < 1. Conversely, the equilibrium point is unstable for R₀ > 1, leading the disease to persist in the community. A sensitivity analysis of the model parameters on the basic reproduction number is performed to study their significance in disease transmission. Numerical simulations are presented graphically to validate the mathematical results.