Global stability in a SQIR epidemic model with ecological environment and stage structure
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Global stability in a SQIR epidemic model with ecological environment and stage structure
Acta Scientiarum Naturalium Universitatis SunYatseniVol. 55, Issue 3, Pages: 47-51(2016)
作者机构:
1. 福建师范大学闽南科技学院,福建,泉州,362332
2.
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Published:2016,
Published Online:25 May 2016,
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FU Jinbo, CHEN Lansun. Global stability in a SQIR epidemic model with ecological environment and stage structure. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(3):47-51(2016)
DOI:
FU Jinbo, CHEN Lansun. Global stability in a SQIR epidemic model with ecological environment and stage structure. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 55(3):47-51(2016)DOI:
Global stability in a SQIR epidemic model with ecological environment and stage structure
a class of SQIR epidemic model with ecological environment and stage-structure is established
in which the population is divided into two life stages-mature and immature
and the viruses spread only in adult population
while the susceptible group of adult population and active sub adult group of immature population are insulated from the infected area by adopting control strategy. By means of qualitative method and stability method of ordinary differential equations
the boundedness of the model and the existence of nonnegative equilibrium point are analyzed. By constructing proper Lyapunov function and limit system theory
sufficient conditions of the global asymptotic stability of the trivial equilibrium point
disease-free equilibrium point and endemic equilibrium point are obtained. The results show that: when the basic reproduction number is less than or equal to 1
all populations tend to be extinct; when the basic reproduction number is greater than 1 and satisfy certain conditions
the viruses will be cleared; when the dominant regeneration number of the viruses is greater than 1 and satisfy certain conditions
the viruses continue to prevail and will become a local disease.