Analyzing the impact of prevention strategies of a fractional order malaria model using Adam–Bashforth approach

Abstract

Even though there is a malaria vaccine for children under-five, malaria continues to be one of the deadly diseases in Sub-Sahara Africa. Nonetheless, there are varieties of preventive measures that, when properly used, can serve as a sort of vaccination and aid in the eradication process. The proportion of persons who must follow the preventive measures ($\pi$) is crucial in the battle to eradicate malaria. In this study, we provide a mathematical model of Caputo fractional order that captures the dynamics of malaria transmission with an emphasis on preventive measures. For the analysis of the model’s solution, the fixed point theorem is utilized to determine the existence and uniqueness of the solution with Ulam–Hyers stability. It has been observed that increasing $\pi$ reduces the infected human and vector population. It was proven that a closed community may eventually control or possibly eradicate malaria by reducing both transmission rates and increasing preventive rates. Also, if the preventive strategies campaign is intensified and more than 50% of the human population in contiguous communities in the region acting in concert implement these, then a marked reduction should be seen in the infected vector population leading to a complete eradication of malaria in the region. In order to find the numerical trajectories of the caputo fractional order, the Adam–Bashforth approach scheme is used.