The epidemic characteristics, including the epidemic final size, peak, andturning point, of two classical SIR models with disease-induced death are investigated when asmall initial value of the infective population is released. The models have mass-action (i.e.bilinear), or density dependent (i.e. standard) incidence, respectively. For the two models, theconditions that determining whether the related epidemic characteristics of an epidemicoutbreak appear are explicitly determine by rigorous mathematical analysis. The dependenceof the epidemic final size on the initial values of the infective class is demonstrated. The peak,turning point (if it exists) and the corresponding time are found. The obtained results suggestthat their basic reproduction numbers are one factor determining the epidemic characteristics,but not the only one. The characteristics of the two models depend on the initial values andproportions of various compartments as well. At last, the similarities and differences of theepidemic characteristics between the two models are discussed.
Citation: Jianquan Li, Yiqun Li, Yali Yang. Epidemic characteristics of two classic models and the dependence on the initial conditions[J]. Mathematical Biosciences and Engineering, 2016, 13(5): 999-1010. doi: 10.3934/mbe.2016027
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The epidemic characteristics, including the epidemic final size, peak, andturning point, of two classical SIR models with disease-induced death are investigated when asmall initial value of the infective population is released. The models have mass-action (i.e.bilinear), or density dependent (i.e. standard) incidence, respectively. For the two models, theconditions that determining whether the related epidemic characteristics of an epidemicoutbreak appear are explicitly determine by rigorous mathematical analysis. The dependenceof the epidemic final size on the initial values of the infective class is demonstrated. The peak,turning point (if it exists) and the corresponding time are found. The obtained results suggestthat their basic reproduction numbers are one factor determining the epidemic characteristics,but not the only one. The characteristics of the two models depend on the initial values andproportions of various compartments as well. At last, the similarities and differences of theepidemic characteristics between the two models are discussed.
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| 1. | Fengqin Zhang, Jianquan Li, Jia Li, Epidemic characteristics of two classic SIS models with disease-induced death, 2017, 424, 00225193, 73, 10.1016/j.jtbi.2017.04.029 | |
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Jianquan Li, Yiqun Li, Yali Yang. Epidemic characteristics of two classic models and the dependence on the initial conditions[J]. Mathematical Biosciences and Engineering, 2016, 13(5): 999-1010. doi: 10.3934/mbe.2016027
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