van den Driessche, P.; Watmough, James Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. (English) Zbl 1015.92036 Math. Biosci. 180, 29-48 (2002). Summary: A precise definition of the basic reproduction number, \(\mathcal R_0\), is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if \(\mathcal R_0<1\) , then the disease free equilibrium is locally asymptotically stable; whereas if \(\mathcal R_0>1\), then it is unstable. Thus, \({\mathcal R}_0\) is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for \(\mathcal R_0\) near one. This criterion, together with the definition of \(\mathcal R_0\), is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control. Cited in 3 ReviewsCited in 3378 Documents MSC: 92D30 Epidemiology 34C60 Qualitative investigation and simulation of ordinary differential equation models Keywords:basic reproduction number; sub-threshold equilibrium; disease transmission model; disease control × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Hethcote, H. W., The mathematics of infectious diseases, SIAM Rev., 42, 599 (2000) · Zbl 0993.92033 [2] Diekmann, O.; Heesterbeek, J. A.P.; Metz, J. A.J., On the definition and the computation of the basic reproduction ratio \(R_0\) in models for infectious diseases in heterogeneous populations, J. Math. 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