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Multi-patch multi-group epidemic model with varying infectivity

Probability, Uncertainty and Quantitative Risk 2022年第4期7卷 333-364页

作者： Raphaël Forien Guodong Pang Étienne Pardoux INRAE Centre INRAE PACADomaine St-Paul-Site Agroparc84914 Avignon CedexFrance Department of Computational Applied Mathematics and Operations Research George R.Brown College of EngineeringRice UniversityHoustonTX 77005US Aix Marseille University CNRSI2M13453 MarseilleFrance

This paper presents a law of large numbers result,as the size of the population tends to infinity,of SIR stochastic epidemic models,for a population distributed over distinct patches(with migrations between them)and distinct groups(possibly age groups).The limit is a set of Volterra-type integral equations,and the result shows the effects of both spatial and population *** novelty of the model is that the infectivity of an infected individual is infection age *** precisely,to each infected individual is attached a random infection-age dependent infectivity function,such that the various random functions attached to distinct individuals are *** proof involves a novel construction of a sequence of *** to invoke the law of large numbers for processes in,by using the solution of a MacKean-Vlasov type Poisson-driven stochastic equation(as in the propagation of chaos theory).We also establish an identity using the Feynman-Kac formula for an adjoint backward *** advantage of this approach is that it assumes much weaker conditions on the random infectivity functions than our earlier work for the homogeneous model in[20],where standard tightness criteria for convergence of stochastic processes were *** illustrate this new approach,we first explain the new proof under the weak assumptions for the homogeneous model,and then describe the multipatch-multigroup model and prove the law of large numbers for that model.

关键词： Stochastic epidemic model Multi-patch multi-group varying infectivity SIR model Law of large numbers Feynman-Kac formula Poisson-driven(McKean-Vlasov type)stochastic equations Propagation of chaos

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