136 research outputs found
Competitive Exclusion and Coexistence of Pathogens in a Homosexually-Transmitted Disease Model
A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population has been studied completely by Jiang and Chai in (J Math Biol 56:373–390, 2008). In this paper, we give a analysis for a SIS STD with two competing strains, where populations are divided into three differential groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterizes competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability about these equilibria under some assumptions. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium, that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability, the coexistence equilibrium is globally stable or unstable if and only if the two boundary equilibria are both unstable or both stable
Mathematical analysis of complex SIR model with coinfection and density dependence
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 disease in the population. We prove that for small carrying capacity
there exist a globally stable disease free equilibrium point. Furthermore, we
establish the continuity of the transition dynamics of the stable equilibrium
point, i.e. we prove that (1) for small values of there exists a unique
globally stable equilibrium point, and (b) it moves continuously as is
growing (while its face type may change). This indicate that carrying capacity
is the crucial parameter and increase in resources in terms of carrying
capacity promotes the risk of infection.Comment: 14 page
The effect of co-colonization with community-acquired and hospital-acquired methicillin-resistant Staphylococcus aureus strains on competitive exclusion
We investigate the in-hospital transmission dynamics of two methicillin-resistant Staphylococcus aureus(MRSA) strains: hospital-acquired methicillin resistant S. aureus (HA-MRSA) and community-acquired methicillin-resistant S. aureus (CA-MRSA). Under the assumption that patients can only be colonized with one strain of MRSA at a time, global results show that competitive exclusion occurs between HA-MRSA and CA-MRSA strains; the strain with the larger basic reproduction ratio will become endemic while the other is extinguished due to competition. Because new studies suggest that patients can be concurrently colonized with multiple strains of MRSA, we extend the model to allow patients to be co-colonized with HA-MRSA and CA-MRSA. Using the extended model, we explore the effect of co-colonization on competitive exclusion by determining the invasion reproduction ratios of the boundary equilibria. In contrast to results derived from the assumption that co-colonization does not occur, the extended model rarely exhibits competitive exclusion. More commonly, both strains become endemic in the hospital. When transmission rates are assumed equal and decolonization measures act equally on all strains, competitive exclusion never occurs. Other interesting phenomena are exhibited. For example, solutions can tend toward a co-existence equilibrium, even when the basic reproduction ratio of one of the strains is less than one
A Discrete-time Networked Competitive Bivirus SIS Model
The paper deals with the analysis of a discrete-time networked competitive
bivirus susceptible-infected-susceptible (SIS) model. More specifically, we
suppose that virus 1 and virus 2 are circulating in the population and are in
competition with each other. We show that the model is strongly monotone, and
that, under certain assumptions, it does not admit any periodic orbit. We
identify a sufficient condition for exponential convergence to the disease-free
equilibrium (DFE). Assuming only virus 1 (resp. virus 2) is alive, we establish
a condition for global asymptotic convergence to the single-virus endemic
equilibrium of virus 1 (resp. virus 2) -- our proof does not rely on the
construction of a Lyapunov function. Assuming both virus 1 and virus 2 are
alive, we establish a condition which ensures local exponential convergence to
the single-virus equilibrium of virus 1 (resp. virus 2). Finally, we provide a
sufficient (resp. necessary) condition for the existence of a coexistence
equilibrium
The optimal treatment of an infectious disease with two strains
This paper explores the optimal treatment of an infectious disease in a Susceptible-Infected-Susceptible model, where there are two strains of the disease and one strain is more infectious than the other. The strains are perfectly distinguishable, instantly diagnosed and equally costly in terms of social welfare. Treatment is equally costly and effective for both strains. Eradication is not possible, and there is no superinfection. In this model, we characterise two types of fixed points: coexistence equilibria, where both strains prevail, and boundary equilibria, where one strain is asymptotically eradicated and the other prevails at a positive level. We derive regimes of feasibility that determine which equilibria are feasible for which parameter combinations. Numerically, we show that optimal policy exhibits switch points over time, and that the paths to coexistence equilibria exhibit spirals, suggesting that coexistence equilibria are never the end points of optimal paths
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