期刊
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
卷 9, 期 3, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S1793524516500467
关键词
SIR model; heterogeneity; nonlinear incidence rate; time delays; global stability; Lyapunov functional
资金
- National Natural Science Foundation of China [11371112, 11401182, 11101104]
- Heilongjiang Provincial Natural Science Foundation [A201208]
- Fundamental Research Funds for the Central Universities [HIT. IBRSEM. A.201401, HIT. IBRSEM. 201332]
To investigate the effect of heterogeneity on the global dynamics of two SIR epidemic models with general nonlinear incidence rate and infection delays, we formulate a multi-group model corresponding to the heterogeneity in the host population and a multi-stage model corresponding to heterogeneous stages of infection. Under biologically motivated considerations, we establish that the global dynamics for each of the two models is determined completely by the corresponding basic reproduction number: if the basic reproduction number is less than or equal to one, then the disease-free equilibrium is globally asymptotically stable and the disease dies out in all groups or stages; if the basic reproduction number is larger than one, then the disease will persist in all groups or stages, and there is a unique endemic equilibrium which is globally asymptotically stable. Then we conclude that the heterogeneity does not change the global dynamics of the SIR model when the incidence rate is a general nonlinear function. Our results extend a class of previous results and can be applied to the other epidemiological models. The proofs of the main results use Lyapunov functional and graph-theoretic approach.
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