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2009•Journal of the University of Shanghai for Science and TechnologyRequires access

A kind of combined epidemic models of SEIR and SEIS with varying total population size

Sanling Yuan

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Abstract

A kind of combined epidemic models of SEIR and SEIS with exponential birth rate and standard incidence was studied.The threshold is identified which determines the outcome of disease is given and the existence of the equilibrium are discussed.By the means of stable theory and autonomous convergent theory,this paper proves global asymptotical stability of the disease-free equilibrium when taking no account of the disease-caused rate.The global asymptotical stability of the endemic equilibrium is proved using autonomous convergent theory when there's no disease-caused person.

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What this paper is about

A kind of combined epidemic models of SEIR and SEIS with exponential birth rate and standard incidence was studied.The threshold is identified which determines the outcome of disease is given and the existence of the equilibrium are discussed.By the means of stable theory and autonomous convergent theory,this paper proves global asymptotical stability of the disease-free equilibrium when taking no account of the disease-caused rate.The global asymptotical stability of the endemic equilibrium is proved using autonomous convergent theory when there's no disease-caused person.

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Available abstract

A kind of combined epidemic models of SEIR and SEIS with exponential birth rate and standard incidence was studied.The threshold is identified which determines the outcome of disease is given and the existence of the equilibrium are discussed.By the means of stable theory and autonomous convergent theory,this paper proves global asymptotical stability of the disease-free equilibrium when taking no account of the disease-caused rate.The global asymptotical stability of the endemic equilibrium is proved using autonomous convergent theory when there's no disease-caused person.

Key concepts: Epidemic model, Mathematics, Stability (learning theory), Exponential stability, Applied mathematics, Outcome (game theory), Exponential growth, Population

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