A computational framework for evaluating the role of mobility on the propagation of epidemics on point processes

• Published in: Journal of mathematical biology Vol. 84; no. 1-2; p. 4
• Main Authors: Baccelli, François, Ramesan, Nithin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2022; Springer Nature B.V; Springer
• Subjects: Applications of Mathematics; Communicable Diseases - epidemiology; Computer applications; Computer Science; Conservation equations; Disease Susceptibility - epidemiology; Epidemics; Euclidean geometry; Extinction; Humans; Infections; Mathematical and Computational Biology; Mathematical models; Mathematics; Mathematics and Statistics; Models, Biological; Networking and Internet Architecture; Parameters; Phase diagrams; Polynomials; Population Density; Probability; Reproduction; Simulation; Survival; Toruses; Epidemic; Markov process; Motion; 60G55; Phase diagram; Contact process; Boolean model; Shot-noise process; 92D30; Point process; Stationary regime; SIS model; 60K35; Moment measures
• ISSN: 0303-6812; 1432-1416; 1432-1416
• DOI: 10.1007/s00285-021-01692-1

This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of the paper is a model where points are also subject to some random motion. Conservation equations for moment measures are leveraged to analyze the stationary regime of the point processes of infected and susceptible individuals. A heuristic factorization of the third moment measure is then proposed to obtain simple polynomial equations allowing one to derive closed form approximations for the fraction of infected individuals in the steady state. These polynomial equations also lead to a phase diagram which tentatively delineates the regions of the space of parameters (population density, infection radius, infection and recovery rate, and motion rate) where the epidemic survives and those where there is extinction. A key take-away from this phase diagram is that the extinction of the epidemic is not always aided by a decrease in the motion rate. These results are substantiated by simulations on large two dimensional tori. These simulations show that the polynomial equations accurately predict the fraction of infected individuals when the epidemic survives. The simulations also show that the proposed phase diagram accurately predicts the parameter regions where the mean survival time of the epidemic increases (resp. decreases) with motion rate.