A Mathematical Model for Effective Control and Possible Eradication of Malaria

Abstract

In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies α and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort α was found to be the most sensitive parameter in the reduction of ℛ 0 . Hence, numerical simulations were performed using different values of α to determine an optimal value of α that reduces the incidence rate fastest. It was discovered that an optimal combination that reduces the incidence rate fastest comes from about 40 % of adherence to the preventive strategies coupled with about 40 % of infected humans seeking clinical treatment, as this will reduce the infected human and vector populations considerably.

A fractional order Monkeypox model with protected travelers using the fixed point theorem and Newton polynomial interpolation

“…Application of Mathematics in modelling of infectious diseases and constructive analytical study together with numerical simulations have contributed immensely to understanding diseases dynamics and their possible effective control and eradication measures [25] , [26] . It plays an important role in informing policymakers and management decisions on infectious diseases [27] .…”

Mathematical and Stability Analysis of Dengue–Malaria Co-Infection with Disease Control Strategies

“…Malaria has a more dangerous and ancient history than other mosquito-borne diseases like dengue. According to the WHO malaria report, the number of malaria cases increased from 216 million in 2016 to 320 million in 2017 [15,16] and reported around 241 million malaria cases globally, with 627,000 malaria deaths predicted in 2020 [17]. Africa was the dominant region in 2020, with 95% of malaria cases and 96% of malaria deaths [17,18].…”

“…The common symptoms of malaria include fever, sweating, shivering or cold, vomiting, headache, diarrhea, and muscle aches. The latent period of malaria lasts from 7 to 14 days [14][15][16][17][18][19].…”

“…Various mathematical models exist for malaria as well, each based on different assumptions and control strategies, such as those presented in [15][16][17]. In [15], the focus was on mathematical modeling and two control strategies: human precautions and mosquito sprays.…”

“…Various mathematical models exist for malaria as well, each based on different assumptions and control strategies, such as those presented in [15][16][17]. In [15], the focus was on mathematical modeling and two control strategies: human precautions and mosquito sprays. Both strategies exert a noteworthy influence on disease control; however, selfprecaution emerges as the more efficacious approach.…”