Modelling arthropod active dispersal using Partial differential equations: the case of the mosquito Aedes albopictus

Dispersal is an important driver for animal population dynamics. Insect dispersal is conventionally assessed by Mark-Release-Recapture (MRR) experiments, whose results are usually analyzed by regression or Bayesian approaches which do not incorporate relevant parameters affecting this behavior, such as time dependence and mortality. Here we present an advanced mathematical-statistical method based on partial differential equations (PDEs) to predict dispersal based on MRR data, taking into consideration time, space, and daily mortality. As a case study, the model is applied to estimate the dispersal of the mosquito vector Aedes albopictus using data from three field MRR experiments. We used a two-dimensional PDE heat equation, a normal bivariate distribution, where we incorporated the survival and capture processes. We developed a stochastic model by specifying a likelihood function, with Poisson distribution, to calibrate the model free parameters, including the diffusion coefficient. We then computed quantities of interested as function of space and time, such as the area travelled in unit time. Results show that the PDE approach allowed to compute time dependent measurement of dispersal. In the case study, the model well reproduces the observed recapture process as 86%, 78% and 84% of the experimental observations lie within the 95% CI of the model predictions in the three releases, respectively. The estimated mean values diffusion coefficient are 1,800 (95% CI: 1,704–1 896), 960 (95% CI: 912- 1 128), 552 (95% CI 432–1 080) m2/day for MRR1, MRR2 and MRR3, respectively. The incorporation of time, space, and daily mortality in a single equation provides a more realistic representation of the dispersal process than conventional Bayesian methods and can be easily adapted to estimate the dispersal of insect species of public health and economic relevance. A more realistic prediction of vector species movement will improve the modelling of diseases spread and the effectiveness of control strategies against vectors and pests.