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Number of infections suffered by a focal individual in a two‐strain SIS model with partial cross‐immunity
Author(s) -
Almaraz Elena,
GómezCorral Antonio
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5652
Subject(s) - mathematics , outbreak , type (biology) , immunity , strain (injury) , joint probability distribution , function (biology) , immunology , statistics , medicine , biology , virology , immune system , evolutionary biology , ecology
We study a stochastic model for the spread of two pathogen strains—termed type 1 and type 2 —among a homogeneously mixing community consisting of a finite number of individuals. In the model, we assume partial cross‐immunity, exogenous streams of infection, and that the degree of severity of a newly infective individual depends on who this infective individual was infected by. The aim is to characterize the joint probability distribution of the numbers M 1 and M 2 of type‐1 and type‐2 infections suffered by a focal individual during an outbreak of the disease. We present iterative procedures for computing the probability mass function of ( M 1 , M 2 ) under the assumption that the initial state of the focal individual is known, and a numerical study of the model is performed to investigate the influence of certain key parameters on the spread of resistant bacteria in hospitals.