Mathematical Modelling and Bifurcation Analysis of Human-Mosquito Interactions for Malaria Control in Bangladesh

Malaria, an infectious disease caused by parasites and transmitted by Anopheles mosquitoes, affects individuals of all ages globally, including Bangladesh. In this work, we develop a transmission dynamics of malaria model between humans and mosquitoes and analyze its properties and solutions. Using the Next-Generation Matrix methods, our estimation of the fundamental reproduction number, R₀, shows that malaria spontaneously ends when R₀ is smaller than 1. On the other hand, malaria continues to exist within the populace if R₀ is larger than 1. We calibrate our proposed model with Bangladeshi malaria incidence data from 2010 to 2022 to estimate some model parameters. We also performed numerical analysis to support our analytic results and explored the impact of different parameters, finding that the infection dynamics are highly sensitive to variations in the transmission rates and the basic reproduction number, R0 . Specifically, when R0 < 1, the disease tends to die out with lower levels of infected individuals in both human and mosquito populations, whereas for R0 > 1, the infection spreads rapidly, leading to higher infection levels. Furthermore, higher human-to-mosquito transmission rates and loss of immunity significantly intensify the spread of malaria, emphasizing the need for targeted interventions. On the other hand, increased disease-related and recovery rates help reduce transmission. We used the sensitivity index to measure how the model's output changes in response to its input parameters. The results indicate that the rates of mosquito and human interaction significantly impact the prevalence of malaria. Finally, we performed a bifurcation analysis to explore the corresponding model parameters and demonstrated the stability of the situation. The findings of this analysis give policymakers guidance regarding the best course of action for reducing the burden of malaria in Bangladesh.