Coinfection dynamics of two diseases in a single host population

Gao, Daozhou; Porco, Travis C.; Ruan, Shigui

doi:10.1016/j.jmaa.2016.04.039

Cited by 43 publications

(37 citation statements)

References 61 publications

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“…One of the most significant aspects of studying multistrain epidemic models is to identify those conditions that lead to the coexistence of different strains. The dynamics of coinfection are important in this case, because in case of co‐infection, treatment against one strain may agitate the other …”

Section: Introductionmentioning

confidence: 99%

“…Stability analysis was performed to identify conditions for the coexistence and competitive exclusion of the two strains. Gao et al study an SIS model with dual infection. Simultaneous transmission of infection and no immunity have been considered.…”

Section: Introductionmentioning

confidence: 99%

“…The model was formulated, and some of our results were recently announced in Ghersheen et al We analyse the model with the possibility of transmission of two strains simultaneously. However, contrary to Gao et al, to diminish the complexity of model and to study the global behaviour of the system, the reduction of the system is needed to some sense. So we assume that there is no interaction between single strains, since the coinfected class is always the largest class.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

Ghersheen

Kozlov

Tkachev

et al. 2019

Math Methods in App Sciences

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Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection are important in this case. We formulated an susceptible infected recovered (SIR) model that describes the coinfection of the two viral strains in a single host population with an addition of limited growth of susceptible in terms of carrying capacity. The model describes five classes of a population: susceptible, infected by first virus, infected by second virus, infected by both viruses, and completely immune class. We proved that for any set of parameter values, there exists a globally stable equilibrium point. This guarantees that the disease always persists in the population with a deeper connection between the intensity of infection and carrying capacity of population. Increase in resources in terms of carrying capacity promotes the risk of infection, which may lead to destabilization of the population.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

Ghersheen

Kozlov

Tkachev

et al. 2019

Math Methods in App Sciences

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“…However, there is also a risk that one reaches the boarder of what is actually possible to analyze. Previously, Allen et al studied an SI model with density‐dependent mortality and coinfection in a single host where one strain is vertical transmitted and the other is horizontally transmitted and the model has application on hantavirus and arenavirus, and Gao et al studied an SIS model with dual infection. Simultaneous transmission of infection and no immunity has been considered.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of complex SIR model with coinfection and density dependence

Ghersheen

Kozlov

Tkachev

et al. 2019

Comp and Math Methods

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An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed, and several threshold conditions are obtained, which describes the establishment of diseases in the population. We prove that, for small carrying capacity K, there exists a globally stable disease‐free equilibrium point. Furthermore, we establish the continuity of the transition dynamics of the stable equilibrium point, that is, we prove that, (1) for small values of K, there exists a unique globally stable equilibrium point, and (b) it moves continuously as K is growing (while its face type may change). This indicates that the carrying capacity is the crucial parameter and an increase in resources in terms of carrying capacity promotes the risk of infection.

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“…Proof of Theorem 3.1 The calculation of boundary equilibria for the community equations (2.2) is straightforward and simple except that of E 13 and E 23 which can be found in Gao et al [16]. So we will only focus on the stability analysis.…”

Section: A Proof Of Theorem 31mentioning

confidence: 99%

Antibiotic resistance as collateral damage: The tragedy of the commons in a two-disease setting

Gao

Lietman

Porco

2015

Mathematical Biosciences

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We propose a simple two-disease epidemic model where one disease exhibits only a drug-sensitive strain, while the other exhibits both drug-sensitive and drug-resistant strains. Treatment for the first disease may select for resistance in the other. We model antibiotic use as a mathematical game through the study of individual incentives and community welfare. The basic reproduction number is derived and the existence and local stability of the model equilibria are analyzed. When the force of infection of each disease is unaffected by the presence of the other, we find that there is a conflict of interest between individual and community, known as a tragedy of the commons, under targeted treatment towards persons infected by the single strain disease, but there is no conflict under mass treatment. However, we numerically show that individual and social incentive to use antibiotics may show disaccord under mass treatment if the restriction on the transmission ability of the dually infected people is removed, or drug resistant infection is worse than drug sensitive infection, or the uninfected state has a comparative disutility over the infected states.

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Coinfection dynamics of two diseases in a single host population

Cited by 43 publications

References 61 publications

Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity

Mathematical analysis of complex SIR model with coinfection and density dependence

Antibiotic resistance as collateral damage: The tragedy of the commons in a two-disease setting

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