Dynamics and Simulations of Impulsive Population Models Involving Integrated Mosquito Control Strategies and Fractional Derivatives for Dengue Control

Dengue fever, a mosquito-borne disease caused by the dengue virus, imposes a substantial disease burden on the world. Wolbachia not only manipulates the reproductive processes of mosquitoes through maternal inheritance and cytoplasmic incompatibility (CI) but also restrain the replication of dengue viruses within mosquitoes, becoming a novel approach for biologically combating dengue fever. A combined use of Wolbachia and insecticides may help to prevent pesky mosquito bites and dengue transmission. A model with impulsive spraying insecticide is introduced to examine the spread of Wolbachia in wild mosquitoes. We prove the stability and permanence results of periodic solutions in the system. Partial rank correlation coefficients (PRCCs) can determine the importance of the contribution of input parameters on the value of the outcome variable. PRCCs are used to analyze the influence of input parameters on the threshold condition of the population replacement strategy. We then explore the impacts of mosquito-killing rates and pulse periods on both population eradication and replacement strategies. To further investigate the effects of memory intensity on the two control strategies, we developed a Caputo fractional-order impulsive mosquito population model with integrated control measures. Simulation results show that for the low fecundity scenario of individuals, as memory intensity increases, the mosquito eradication strategy will occur at a slower speed, potentially even leading to the mosquito replacement strategy with low female numbers. For the high fecundity scenario of individuals, with increasing memory intensity, the mosquito replacement strategy will be achieved more quickly, with lower mosquito population amplitudes and overall numbers. It indicates that although memory factors are not conducive to implementing a mosquito eradication strategy, achieving the replacement strategy with a lower mosquito amount is helpful. This work will be advantageous for developing efficient integrated control strategies to curb dengue transmission.