Modelling a Wolbachia Invasion Using a Slow–Fast Dispersal Reaction–Diffusion Approach

Abstract

This paper uses a reaction-diffusion approach to examine the dynamics in the spread of a Wolbachia infection within a population of mosquitoes in a homogeneous environment. The formulated model builds upon an earlier model by Skalski and Gilliam (Am. Nat. 161(3):441-458, 2003), which incorporates a slow and fast dispersal mode. This generates a faster wavespeed than previous reaction-diffusion approaches, which have been found to produce wavespeeds that are unrealistically slow when compared with direct observations. In addition, the model incorporates cytoplasmic incompatibility between male and female mosquitoes, which creates a strong Allee effect in the dynamics. In previous studies, linearised wavespeeds have been found to be inaccurate when a strong Allee effect is underpinning the dynamics. We provide a means to approximate the wavespeed generated by the model and show that it is in close agreement with numerical simulations. Wavespeeds are approximated for both Aedes aegypti and Drosophila simulans mosquitoes at different temperatures. These wavespeeds indicate that as the temperature decreases within the optimal temperature range for mosquito survival, the speed of a Wolbachia invasion increases for Aedes aegypti populations and decreases for Drosophila simulans populations.

Population dynamics of underdominance gene drive systems in continuous space

“…It was found in this study that the release threshold required for successful invasion varied based on the exact pattern of release in a simple spatially-explicit population (central vs patchy, small area vs. large area), and that this threshold was different from panmictic populations. That spatial structure could critically impact the behavior of an underdominance system is also suggested by modeling studies of Wolbachia systems, which share threshold-dependent dynamics with underdominance systems and have been shown to exhibit distinct dynamics in spatial models [19][20][21][22][23][24][25][26][27][28] .…”

Controlling Aedes aegypti populations by limited Wolbachia‐based strategies in a seasonal environment

“…These studies result in complex systems representing empiric mathematical models, based on a multidisciplinary approach, integrating specialized theoretical knowledge, computational, and field/laboratory experience. ()…”

“…These studies result in complex systems representing empiric mathematical models, based on a multidisciplinary approach, integrating specialized theoretical knowledge, computational, and field/laboratory experience. [8][9][10][11][12][13] The mathematical models help to formulate better control strategies, more efficient and economically viable. Two recent papers, proposed by Bliman et al 14 and Campo-Duarte et al, 15 consider the introduction of Wolbachia-infected mosquitoes to control the population of wild mosquitoes using different models without seasonality.…”

Investigating the Reproducibility of In Vitro Cell Biology Assays Using Mathematical Models

“…14,000 10000 ± 1000 0.049 ± 0.001 14.15 16,000 6100 ± 3000 0.049 ± 0.003 14. The location ofD andλ in each case is shown as a red square.…”

“…Population dynamics and population growth are also central to understanding the spread of infectious diseases. For example, the spread of Wolbachia into wild mosquito populations is thought to reduce a wide range of diseases, and the spatial spreading of the mosquito population is partly driven by the population dynamics of the mosquito population [16]. Similar ideas also apply to the spreading of tumour cells and the progression of cancer, which is related to the rates of proliferation of invasive cancer cells [4,78,92].…”