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In this chapter, an application of Mathematical Epidemiology to crop vector-borne diseases is presented to investigate the interactions between crops, vectors, and virus. The main illustrative example is the cassava mosaic disease (CMD).…
We show the existence of traveling front solutions in a diffusive classical SIS epidemic model and the SIS model with a saturating incidence in the size of the susceptible population. We investigate the situation where both susceptible and…
We introduce and study a model stemming from game theory for the spread of an epidemic throughout a given population. Each agent is allowed to choose an action whose value dictates to what extent they limit their social interactions, if at…
We consider two approaches to study the spread of infectious diseases within a spatially structured population distributed in social clusters. According whether we consider only the population of infected individuals or both populations of…
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…
It is the main purpose of this paper to introduce a graph-valued stochastic process in order to model the spread of a communicable infectious disease. The major novelty of the SIR model we promote lies in the fact that the social network on…
In the continuity of a recent paper ([6]), dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact…
We study the rate of weak convergence of Markov chains to diffusion processes under suitable but quite general assumptions. We give an example in the financial framework, applying the convergence analysis to a multiple jumps tree…
In this paper, a stochastic dynamic control strategy is presented to prevent the spread of an infection over a homogeneous network. The infectious process is persistent, i.e., it continues to contaminate the network once it is established.…
The susceptible-infected-susceptible (SIS) agent-based model is usually employed in the investigation of epidemics. The model describes a Markov process for a single communicable disease among susceptible (S) and infected (I) agents.…
The scope of this work is to serve as a guiding tool against subjective estimations on real pandemic situations (mainly due to the inability to acquire objective real data over whole populations). The previously introduced model of closed…
A hybrid network--deterministic model for simulation of multiresistant pathogen spread in a healthcare system is presented. The model accounts for two paths of pathogen transmission between the healthcare facilities: inter-hospital patient…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition…
This paper introduces a new approach of treating platoon systems using mean-variance control formulation. The underlying system is a controlled switching diffusion in which the random switching process is a continuous-time Markov chain.…
We study the limit behaviour of a generally non-linear ordinary differential equation whose solution is a superadditive generalisation of a stochastic matrix, and provide necessary and sufficient conditions for this solution to be ergodic,…
A Markovian SIR (Susceptible-Infectious-Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours.…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
Density dependent Markov population processes in large populations of size $N$ were shown by Kurtz (1970, 1971) to be well approximated over finite time intervals by the solution of the differential equations that describe their average…
This document is the Part IV of the book 'Stochastic Epidemic Models with Inference' edited by Tom Britton and Etienne Pardoux. It is written by Catherine Lar\'edo, with the contribution of Viet Chi Tran for the Chapter 4. Epidemic data…