Related papers: Reaction-Diffusion Systems in Epidemiology
The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…
This paper gives an introduction to rule-based modelling applied to topics in infectious diseases. Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in…
Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired…
Mathematical and computational modeling approaches are increasingly used as quantitative tools in the analysis and forecasting of infectious disease epidemics. The growing need for realism in addressing complex public health questions is…
The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative…
This paper examines a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and constant total population. The infection mechanism in the model is described by a nonlinear term of the form…
The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the…
Diffusion processes are governed by external triggers and internal dynamics in complex systems. Timely and cost-effective control of infectious disease spread critically relies on uncovering the underlying diffusion mechanisms, which is…
In order to explore the impact of periodically evolving domain on the transmission of disease, we study a SIS reaction-diffusion model with logistic term on a periodically evolving domain. The basic reproduction number ${\mathcal{R}}_0$ is…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics,…
It is increasingly important to understand the spatial dynamics of epidemics. While there are numerous mathematical models of epidemics, there is a scarcity of physical systems with sufficiently well-controlled parameters to allow…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
The spatial structure of populations is a key element in the understanding of the large scale spreading of epidemics. Motivated by the recent empirical evidence on the heterogeneous properties of transportation and commuting patterns among…
Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the…
Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread…
In this paper, we consider reaction-diffusion epidemic models with mass action or standard incidence mechanism and study the impact of limiting population movement on disease transmissions. We set either the dispersal rate of the…
We show we can control an epidemic reaction-diffusion on a directed, and heterogeneous, network by redirecting the flows, thanks to the optimisation of well-designed loss functions, in particular the basic reproduction number of the model.…
The immune response to a pathogen has two basic features. The first is the expansion of a few pathogen-specific cells to form a population large enough to control the pathogen. The second is the process of differentiation of cells from an…