Mathematical Analysis Of The Two-Patch SIRS-SIW Model For The Dynamical Transmission Of Dengue Fever Involving Wolbachia - Fitriana Saptaningtyas; Fugo Takasu; Hartono; Fithri Lathifah; Ikha Parwitasari (Jambura Journal of Biomathematics (JJBM), 2026)
A promising, biologically safe approach to controlling dengue hemorrhagic fever (DHF) is the release of Wolbachia-infected mosquitoes. The use of mathematical modelling to identify optimal control strategies has been the focus of numerous studies. However, the dynamics of human movement between areas where Wolbachia is applied and areas where it is not remain poorly understood. In this study, the spread of dengue fever is examined through a two-patch autonomous ordinary differential equation system encompassing two human population patches, along with Aedes aegypti mosquitoes and Wolbachia, to characterise the dynamics of dengue transmission between humans interacting from two separate patches, alongside the mosquito populations. The Wolbachia strategy has been implemented in portions of the DIY region. We use a two-patch framework to model this issue. We propose developing a mathematical model to investigate the relationship between mosquito bite rates and the proportion of Wolbachia mosquitoes, while accounting for temporary population movements between spatially distinct patches. We assume that the human population is divided into two distinct patches: one in an area where Wolbachia has been implemented and the other in an area where it has not, with a temporary visit between the patches. We compute the local and global stability criteria for the disease-free equilibrium and the basic reproduction number for each patch. In addition, we conducted a thorough analysis of the key parameters related to the proportion of Wolbachia mosquitoes that affect the stability of this equilibrium point. These parameters may serve as vital references to aid in eradicating dengue hemorrhagic fever (DHF) within each patch. Our findings demonstrate that increasing the number of Wolbachia strains significantly limits the spread of dengue in Yogyakarta. The spread of dengue fever can be suppressed by targeting at least 69.9% of Wolbachia mosquitoes from the total mosquito population.