A Dynamic Investigation to Analyzing Divorce Effects within Wolbachia Models

Abstract

Dengue fever, a mosquito-borne viral disease, poses a significant global health burden with approximately 390 million infections reported in 2016. As insecticide resistance increases, novel vector control methods such as Wolbachia bacteria are being investigated. Wolbachia reduces dengue transmission by decreasing mosquito lifespan and inhibiting viral replication. The mathematical model has demonstrated Wolbachia’s potential to eliminate local dengue transmission. Field trials in Australia and Indonesia have exhibited substantial reductions in dengue incidence following Wolbachia releases. However, concerns remain that these reductions may be transient. This report reviews a mathematical model of Wolbachia for dengue control, evaluating its assumptions and findings. The model indicates Wolbachia could potentially eliminate dengue locally, yet also permit endemic transmission. We propose further analysis of this model to assess the long-term impacts of Wolbachia deployment. Examining the duration of control measures and post-release effects will provide greater insight into Wolbachia’s capacity for sustainable dengue mitigation. The reviewed model comprises a system of seven ordinary differential equations representing a dual Susceptible-Exposed-Infected-Recovered (SEIR) structure for human and mosquito populations. Key assumptions include only modeling female mosquitoes’ post-aquatic life stages and complete cytoplasmic incompatibility of Wolbachia. The basic reproductive number was derived and equilibrium points were identified. This mathematical modeling approach enables the simulation of complex dengue transmission dynamics under various Wolbachia release scenarios. Further analysis can evaluate the potential for the ”honeymoon effect” and ”divorce effect” to undermine the initial successes of Wolbachia trials. This will facilitate a more robust assessment of Wolbachia’s long-term viability as a dengue control strategy.