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We present a comprehensive study of MHD waves and instabilities in a weakly ionised system, e.g., an interstellar molecular cloud. We determine all the critical wavelengths of perturbations across which the sustainable wave modes can change…
Collective cell migration contributes to embryogenesis, wound healing and tumor metastasis. Cell monolayer migration experiments help understanding what determines the movement of cells far from the leading edge. Inhibiting cell…
The goal of this work is to understand and quantify how a line with nonlocal diffusion given by an integral enhances a reaction-diffusion process occurring in the surrounding plane. This is part of a long term programme where we aim at…
Even as the incidence of mosquito-borne diseases like West Nile Virus (WNV) in North America has risen over the past decade, effectively modelling mosquito population density or, the abundance has proven to be a persistent challenge. It is…
Over 50% of the world population is at risk of mosquito-borne diseases. Female Ae. aegypti mosquito species transmit Zika, Dengue, and Chikungunya. The spread of these diseases correlate positively with the vector population, and this…
Malaria is transmitted to vertebrates via a mosquito bite, during which rod-like and crescent-shaped parasites, called sporozoites, are injected into the skin of the host. Searching for a blood capillary to penetrate, sporozoites move…
The key of tip growth in eukaryotes is the polarized distribution on plasma membrane of a particle named ROP1. This distribution is the result of a positive feedback loop, whose mechanism can be described by a Differential Equation…
The relationship between epidemiology, mathematical modeling and computational tools allows to build and test theories on the development and battling of a disease. This PhD thesis is motivated by the study of epidemiological models applied…
It is preliminarily known that Aedes mosquitoes are very close to humans and their dwellings, also give rises to a broad spectrum of diseases: dengue, yellow fever, chikungunya. In this paper, we explore a multi-age-class model for mosquito…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
The Bayesian analysis of infectious disease surveillance data from multiple locations typically involves building and fitting a spatio-temporal model of how the disease spreads in the structured population. Here we present new generally…
This paper presents an age-structured, non-autonomous logistic model describing the aquatic and adult stages of the dynamics of malaria-vector mosquitoes. We propose a biological control strategy targeting the aquatic compartment and…
Insect-borne diseases are diseases carried by insects affecting humans, animals or plants. They have the potential to generate massive outbreaks such as the Zika epidemic in 2015-2016 mostly distributed in the Americas, the Pacific and…
A reaction-diffusion-advection model is proposed and investigated to understand the invasive dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the invasive mosquitoes in a heterogenous…
Dengue is a vector-borne viral disease increasing dramatically over the past years due to improvement in human mobility. The movement of host individuals between and within the patches are captured via a residence-time matrix. A system of…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
With approximately half of the world's population at risk of contracting dengue, this mosquito-borne disease is of global concern. International travellers significantly contribute to dengue's rapid and large-scale spread by importing the…
More than half of the world's population is exposed to the risk of mosquito-borne diseases, which leads to millions of cases and hundreds of thousands of deaths every year. Analyzing this type of data is often complex and poses several…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
How individual dispersal patterns and human intervention behaviours affect the spread of infectious diseases constitutes a central problem in epidemiological research. This paper develops an impulsive nonlocal faecal-oral model with free…