Mechanistic-statistical inference of mosquito dynamics from mark-release-recapture data

TL;DR

The paper develops a mechanistic–statistical framework to infer mosquito dispersal and survival from mark–release–recapture data by coupling a microscopic Itô diffusion model with a macroscopic reaction–diffusion PDE, and embedding this in a Poisson observation model. Inference proceeds via maximum likelihood using PDE-predicted trap captures, with uncertainty quantified through parametric bootstrap based on an IBM, and parameter bounds informed by diffusion scaling. Validation on simulated data shows accurate recovery of movement, mortality, and capture parameters, while application to a Cuban urban MRR campaign yields about five days of post-release life expectancy and a typical displacement near 180 m after five days, with a homogeneous mobility model preferred by AIC. The framework provides biologically interpretable metrics and a principled basis for designing SIT-based interventions, offering a scalable approach for inference in sparse, noisy MRR data and potential extensions to heterogeneous environments and multi-source releases.

Abstract

Biological control strategies against mosquito-borne diseases--such as the sterile insect technique (SIT), RIDL, and Wolbachia-based releases--require reliable estimates of dispersal and survival of released males. We propose a mechanistic--statistical framework for mark--release--recapture (MRR) data linking an individual-based 2D diffusion model with its reaction--diffusion limit. Inference is based on solving the macroscopic system and embedding it in a Poisson observation model for daily trap counts, with uncertainty quantified via a parametric bootstrap. We validate identifiability using simulated data and apply the model to an urban MRR campaign in El Cano (Havana, Cuba) involving four weekly releases of sterile Aedes aegypti males. The best-supported model suggests a mean life expectancy of about five days and a typical displacement of about 180 m. Unlike empirical fits of survival or dispersal, our mechanistic approach jointly estimates movement, mortality, and capture, yielding biologically interpretable parameters and a principled framework for designing and evaluating SIT-based interventions.

Figures (6)

• Figure 1: Satellite view of the El Cano study site (Havana, Cuba). The blue marker indicates the release point; red numbers label the 21 BG-Sentinel traps used for daily recaptures. Urban areas are shaded in yellow, where a distinct diffusion coefficient is assumed in the heterogeneous model. Imagery: Google Earth, © Google 2025; data: © Airbus.
• Figure 2: Solution $h(t,x)$ of the PDE \ref{['eq:EDP_pop_dens']} vs population density obtained from the microscopic model, in a simplified one-dimensional case with a single trap located at $x=q_1=10$. The mobility coefficient is $\sigma(x)= \sigma_1 + (\sigma2 - \sigma1) (1 + \tanh(x + 20))/2$. The parameter values are $x_0=0$, $N_0=10^4$, $1/\nu=$10 days, $1/\gamma=$2 days, $\sigma_1 = 25~\text{m}/\sqrt{\text{day}}$, $\sigma_2 = 20~\text{m}/\sqrt{\text{day}}$.
• Figure 3: (a) Cumulative mosquito population density $c(x)= \int_0^{20} h(s,x)\,ds$ obtained by solving the reaction–diffusion model \ref{['eq:EDP_pop_dens']} with a homogeneous diffusion coefficient and the MLE parameter vector $\Theta^*$. (b) Relative difference $(c_n(x)-c(x))/c_n(x)$ between the cumulative density with trapping (parameters $\Theta^*$) and without trapping ($\gamma=0$, with $\sigma$ and $\nu$ fixed at their MLE values), highlighting the localized impact of traps.
• Figure 4: Observed trap counts (blue circles) versus expected captures (green crosses) predicted by \ref{['eqn:pi']}–\ref{['eq:EDP_pop_dens']} under the homogeneous model with MLE parameters $\Theta^*$. Each panel corresponds to one trap (1–21). All panels share the same axes (days on the $x$-axis; cumulative captures on the $y$-axis), enabling direct comparison across traps.
• Figure 5: Expected number of trapped mosquitoes predicted by the macroscopic model \ref{['eq:EDP_pop_dens']} in one dimension, expressed as $N_0 \, \pi_1(t) = \int_0^t \int_{\mathbb R} f_1(s) \, h(s,x) \, dx \, ds$, compared with the actual number of trapped mosquitoes obtained from one simulation of the microscopic model. The assumptions are the same as in Fig. \ref{['fig:1D']}.