Improving Wolbachia-Based Control Programs in Urban Settings: Insights from Spatial Modeling

TL;DR

This study tackles the challenge of establishing Wolbachia-infected Aedes aegypti in urban settings by developing a spatial two-dimensional PDE framework that accounts for mosquito dispersal, carrying capacity, and maternal transmission. Building on a reduced $2$-ODE model, it analyzes thresholds for invasion and evaluates practical release strategies, including phased releases and pre-release insecticide (thermal fogging). Key findings show that in low-dispersal areas, targeted releases may succeed without pre-release insecticide, while in high-dispersal zones reducing at least $35\%$ of wild mosquitoes accelerates establishment to within nine months; dispersal rates and release batching significantly influence outcomes. The results offer actionable guidance for cost-effective Wolbachia programs, suggesting strategy customization based on local spatial ecology to reduce vector-borne disease burden. These insights can inform urban vector-control policies and be extended to other arboviruses and settings.

Abstract

Arboviral diseases remain a major public health concern, particularly in tropical and subtropical regions where mosquito populations thrive. One promising strategy to curb transmission is the release of Aedes aegypti mosquitoes infected with Wolbachia, a bacterium that reduces their ability to spread viruses. However, past large-scale releases have not always been successful, especially in complex urban settings, where restricted access to certain areas often leads to infection establishment failures and wasted resources. To address this, we developed and analyzed a partial differential equation model that simulates how Wolbachia-infected mosquitoes are established in different urban environments. We also explored strategies to improve their success under constraints on release size and the efficacy level of insecticide used for pre-release interventions. Our findings suggest that targeted releases are most effective in areas with limited mosquito movement without additional insecticide use. In higher mosquito dispersal areas, reducing at least 35% of wild mosquitoes before release significantly improves establishment within nine months. Additionally, distributing releases over 2-5 weekly batches enhances success more than a single large release, even without other interventions. These findings offer practical insights for designing cost-effective and efficient Wolbachia-based mosquito control programs, reducing the burden of mosquito-borne diseases on vulnerable communities.

Figures (7)

• Figure 1: Release shape geometry Graphical representation of the squared exponential release over a 2D domain size of $3000\;meters\times3000\;meters$. The left plot highlights the release over a subset of the domain ($200\;meters\times200\;meters$), while the right plot illustrates the Gaussian release standard deviation of $\sigma_W=35$ meters with respect to the domain center.
• Figure 2: Numerical computation of threshold condition (PDE solver time step $\Delta t=1.78\times 10^{-2}$, diffusion coefficient $D=60\;m^2/day$). Left: fraction of infection curves for different initial release sizes: releasing at the threshold, i.e, $p_{\text{thres}} = 1,072,640$ female mosquitoes (assuming same amount of male mosquitoes are also released), which is approximately $35.7\%$ of the female carrying capacity (black curve), above the threshold (blue curve), and below the threshold (red curve). After a transition period of approximately 250 days, the infection curve at the threshold stabilizes at a level of $0.6$ over an extended period. In contrast, the curves for releases above or below the threshold quickly approach the complete infection or no-infection states, respectively. Right: behavior of the PDE solution for the Wolbachia-infected state variable $w(r,t)$ (at $t=180$ days) when releasing Wolbachia-infected mosquitoes at threshold value (black curve), above threshold (blue curve), and below threshold (red curve). The solution curve at the threshold evolves into a bubble shape at day $180$ and preserves this shape for about four years.
• Figure 3: Heatmap showing the time in months (region labels) and days (right y-axis), required to achieve $90\%$ of Wolbachia infection in a mosquito population, based on a fixed release size of $3,600,000$ female infected mosquitoes (and about the same amount of males) in a $3000m\times3000m$ area. The $x$-axis represents the diffusion coefficient in $m^2/day$, reflecting mosquito dispersal rates, while the $y$-axis indicates the proportion of the wild mosquito population removed through thermal fogging with three different ranges of intensities. The heatmap color code corresponds to the time to reach $90\%$ of infection, with darker shades indicating shorter times. The figure highlights three distinct regions: $0-3$ months (dark), $3-9$ months (intermediate), and more than $9$ months (light). Removing at least $35\%$ (red line) of the uninfected mosquito population ensures $90\%$ infection is reached within nine months, regardless of mosquito dispersal, while lower removal levels lead to longer times, particularly at large diffusion coefficients.
• Figure 4: Heatmap showing the time in months (region labels) and days (right y-axis) required to achieve $90\%$Wolbachia infection in a mosquito population, assuming a restricted level of insecticide efficacy ($35\%$ intensity of thermal fogging) sprayed on uninfected mosquitoes in a $3000\,m \times 3000\,m$ area. The $x$-axis represents the diffusion coefficient in $m^2/\text{day}$, reflecting mosquito dispersal rates. The $y$-axis indicates the percentage of Wolbachia-infected mosquitoes to release with respect to the reference baseline value used in the simulations ($3,600,000$ females and about the same amount of males). The heatmap color code corresponds to the time to reach $90\%$ of infection, with darker shades indicating shorter establishment times. The figure highlights three distinct regions: $0$--$3$ months (dark), $3$--$9$ months (intermediate), and more than $9$ months (light). For diffusion coefficients between $10$--$45\,m^2/\text{day}$, even a small quantity of released mosquitoes can establish infection within $0$--$9$ months. For dispersal rates greater than $45\,m^2/\text{day}$, the dashed white contour line indicates the minimum quantity of Wolbachia-infected mosquitoes that must be released to reach $90\%$ of infection within $9$ months. The horizontal solid red lines indicate example values of dispersal rates and their corresponding release quantities.
• Figure 5: Fraction of Wolbachia infection over time (days). Performance comparison of releasing infected mosquitoes at the threshold level all at once or distributed in $2-5$ weekly batches. The impact of applying a pre-release mitigation strategy (thermal fogging $35\%$) was also evaluated. Domain size $L= 3000\;m\times 3000\;m$. Diffusion coefficient $D= 60\; m^2/$day. The standard deviation of Gaussian release of $\sigma_w=35$ meters.