Modeling and Research on an Immuno-Epidemiological Coupled System with Coinfection

Abstract

In this paper, a two-strain model with coinfection that links immunological and epidemiological dynamics across scales is formulated. On the with-in host scale, the two strains eliminate each other with the strain having the larger immunological reproduction number persisting. However, on the population scale coinfection is a common occurrence. Individuals infected with strain one can become coinfected with strain two and similarly for individuals originally infected with strain two. The immunological reproduction numbers , the epidemiological reproduction numbers and invasion reproduction numbers are computed. Besides the disease-free equilibrium, there are strain one and strain two dominance equilibria. The disease-free equilibrium is locally asymptotically stable when the epidemiological reproduction numbers are smaller than one. In addition, each strain dominance equilibrium is locally asymptotically stable if the corresponding epidemiological reproduction number is larger than one and the invasion reproduction number of the other strain is smaller than one. The coexistence equilibrium exists when all the reproduction numbers are greater than one. Simulations suggest that when both invasion reproduction numbers are smaller than one, bistability occurs with one of the strains persisting or the other, depending on initial conditions.

Modeling Syphilis and HIV Coinfection: A Case Study in the USA

“…Similar strategy was used in another mathematical model with coinfection (Li et al. 2021 ). Gao et al studied a general coinfection model with bilinear incidence.…”

A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US

“…Multi-strain mathematical models have been widely used to investigate the infectious disease dynamics ( Massard et al, 2022 , de León et al, 2022 , Li et al, 2021b , Rong et al, 2007 , Rong et al, 2012 , Li et al, 2021a , Li et al, 2013 , Martcheva, 2009 , Li et al, 2010 , Saucedo and Martcheva, 2017 , Dang et al, 2016 , Duan et al, 2018 , Cai et al, 2013 , Martcheva and Li, 2013 , Martcheva, 2007 , Thomasey and Martcheva, 2008 , Iannelli et al, 2005 , Martcheva et al, 2007 , Martcheva and Pilyugin, 2006 , Qiu et al, 2013 , Martcheva et al, 2008 , Arruda et al, 2021 , Fudolig and Howard, 2020 , Murall et al, 2014 , Poolman et al, 2008 ). Most studied the existence and stability of the disease-free equilibrium (DFE), strain-dominant equilibria and coexistence equilibria.…”

An environmentally-driven two-strain mutualistic coinfection model with coupling transmission in vivo and vitro and humoral immunity

“…It has been proven that plenty of diverse genetic variants can be coexisting in vivo in many viral infections, which would lead to more virulent infections [26]. Some two-strain coupled models have been studied which do not link the interaction between contaminated environment and virus in body [27,28]. Li et al [28] proposed a class of two-strain coinfection coupled model, which mainly focused on the coexistence equilibrium of two strains and the influence of within-host parameters on dynamics between host.…”

“…Usually, most of the multi-strain transmission models assumed that the interaction between two strains is competitive [6,12,27,28]. However, it has been found that the relationship between various strains of pathogen is not only competitive, but also mutualistic, where one variant acts as a helper virus for the other in the latter [29,30].…”