Global analysis of multi-strains SIS, SIR and MSIR epidemic models

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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“…hence, Y 3 = 0 too. This proves that Y = G 1 and proves (15). It follows that any nontrivial equilibrium state Y ≠ G 1 must satisfy…”

Section: Basic Propertiesmentioning

confidence: 52%

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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“…The SI 1 I 2 R model has 3 equilibria ( Bichara et al, 2014 ). One equilibrium is disease free and is stable when…”

Section: Invasion Analysis: Simentioning

confidence: 99%

The influence of social behaviour on competition between virulent pathogen strains

Pharaon

Bauch

2018

Journal of Theoretical Biology

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Infectious disease interventions like contact precautions and vaccination have proven effective in disease control and elimination. The priority given to interventions can depend strongly on how virulent the pathogen is, and interventions may also depend partly for their success on social processes that respond adaptively to disease dynamics. However, mathematical models of competition between pathogen strains with differing natural history profiles typically assume that human behaviour is fixed. Here, our objective is to model the influence of social behaviour on the competition between pathogen strains with differing virulence. We couple a compartmental Susceptible-Infectious-Recovered model for a resident pathogen strain and a mutant strain with higher virulence, with a differential equation of a population where individuals learn to adopt protective behaviour from others according to the prevalence of infection of the two strains and the perceived severity of the respective strains in the population. We perform invasion analysis, time series analysis and phase plane analysis to show that perceived severities of pathogen strains and the efficacy of infection control against them can greatly impact the invasion of more virulent strain. We demonstrate that adaptive social behaviour enables invasion of the mutant strain under plausible epidemiological scenarios, even when the mutant strain has a lower basic reproductive number than the resident strain. Surprisingly, in some situations, increasing the perceived severity of the resident strain can facilitate invasion of the more virulent mutant strain. Our results demonstrate that for certain applications, it may be necessary to include adaptive social behaviour in models of the emergence of virulent pathogens, so that the models can better assist public health efforts to control infectious diseases.

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“…An ordinary differential equations (ODEs) model of coinfection was designed by Zhang et al to study two parasite strains on two different hosts to know the sustainability and proliferation of these strains in response to variability in mode of action of parasites and its host types. Bichara et al proposed Susceptible Infected Suceptible (SIS), SIR, and MSIR models with variable population and n different pathogen strains to study that under generic conditions, a competitive exclusion principle holds. A two‐disease model was also used by Martcheva and Pilyugin to study dynamics of dual infection by considering time of infection of primary disease.…”

Section: Introductionmentioning

confidence: 99%

“…parasites and its host types. Bichara et al 18 proposed Susceptible Infected Suceptible (SIS), SIR, and MSIR models with variable population and n different pathogen strains to study that under generic conditions, a competitive exclusion principle holds. A two-disease model was also used by Martcheva and Pilyugin 19 to study dynamics of dual infection by considering time of infection of primary disease.…”

mentioning

confidence: 99%

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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Global analysis of multi-strains SIS, SIR and MSIR epidemic models

Cited by 75 publications

References 34 publications

Mathematical analysis of complex SIR model with coinfection and density dependence

Mathematical analysis of complex SIR model with coinfection and density dependence

The influence of social behaviour on competition between virulent pathogen strains

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

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