Balancing Economic Cost and Disease Impact: Optimization Models for Wolbachia-Based Dengue Control

TL;DR

This study proposes a mathematical model that captures the dynamics of releasing Wolbachia-carrying mosquitoes and the transmission of dengue in a population, and formulate single- and multi-objective optimization frameworks to minimize the economic costs associated with releasing Wolbachia-infected mosquitoes and the hospitalization costs resulting from dengue infections.

Abstract

Dengue, which affects millions of people each year, is one of the most common diseases transmitted by infected \textit{Aedes aegypti} mosquitoes. In the Philippines, the annual economic cost of dengue infections is estimated at around PHP 17 billion. Previous studies have shown that controlling the population of mosquitoes capable of transmitting the dengue virus can effectively reduce dengue infection rates. This study explores the use of Wolbachia as a strategy for dengue control by targeting mosquitoes. Since the release of Wolbachia-infected mosquitoes involves substantial costs, careful planning is necessary to balance disease control with the associated economic burden. To address this, we propose a mathematical model that captures the dynamics of releasing Wolbachia-carrying mosquitoes and the transmission of dengue in a population. We formulate single- and multi-objective optimization frameworks to minimize the economic costs associated with releasing Wolbachia-infected mosquitoes and the hospitalization costs resulting from dengue infections. This study aims to provide insights into the practical application of Wolbachia-based interventions for controlling dengue transmission. While the analysis is grounded in the Philippine context, the approach is general enough to be applicable to other dengue-endemic countries.

Figures (12)

• Figure 1: Schematic diagram of the dengue transmission model with the presence of Wolbachia. Humans who are susceptible to dengue ($S_h$) become infected ($I_h,J_h$) upon contact with mosquitoes that carry dengue ($I_v^W$) at a rate of $BC_{vh}$ or $BC_{vh}^w$. Mosquitoes who are susceptible to dengue ($S_v^W$) become infected ($I_v^W$) upon contact with nonhealthcare-seeking humans. Those in $I_h$ recover at a rate of $\gamma$ while those in $J_h$ recover at a rate of $\theta$. $^*$Transmission dynamics for Wolbachia in $S_v^W$ and $I_v^W$ is demonstrated in Figure \ref{['transmission']}.
• Figure 2: Transmission dynamics of Wolbachia on $S_v^W$. We note that similar dynamics are observed on $I_v^W$. Mosquitoes in the $S_{vf}^w$ compartment transition into $S_{vfp}^w$ at a rate of $\sigma$. Mosquitoes in the $S_{vf}$ compartment transition into either $S_{vfp}$ or $S_{vfp}^s$ at a rate of $\sigma m$ or $\sigma m_w$, respectively. Mosquitoes in the $S_{vfp}$ compartment lay uninfected eggs ($A$) at a rate of $\eta$ while mosquitoes in the $S_{vfp}^w$ lay either Wolbachia-infected ($A^w$) or uninfected eggs at a rate of $\eta_w v_w$ or $\eta_w v$, respectively. Wolbachia-infected eggs eventually develop into Wolbachia-infected male ($M_v^w$) and (dengue susceptible) infected nonpregnant female mosquitoes while Wolbachia-uninfected eggs develop into Wolbachia-uninfected male ($M_v$) and (dengue susceptible) nonpregnant female mosquitoes. We consider a release $r(t)$ of Wolbachia-infected eggs.
• Figure 3: Different release schemes: constant release (blue); linear and decreasing release, which simulates a peak at the start of the release period (orange); and a bump release, which simulates a peak at a later day—specifically, day 50 (yellow) or day 100 (violet). The number of hospitalized individuals under these different forms of $r(t)$ is shown for the case in which all release schemes have the same peak.
• Figure 4: The number of hospitalized individuals under the different forms of $r(t)$ for the case in which all release schemes have the same total number of Wolbachia-infected larva released over time.
• Figure 5: Optimal release schedule and its effect on healthcare-seeking individuals

Theorems & Definitions (6)

• Theorem 3.1: Existence and uniqueness of solutions
• proof
• Theorem 3.2: Forward invariance
• proof
• Theorem 4.1
• proof