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COMPUTATION OF ℛ IN AGE-STRUCTURED EPIDEMIOLOGICAL MODELS WITH MATERNAL AND TEMPORARY IMMUNITY
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Nov 01 2015
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Source: Discrete Continuous Dyn Syst Ser B. 21(2):399-415.
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Alternative Title:Discrete Continuous Dyn Syst Ser B
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Description:For infectious diseases such as pertussis, susceptibility is determined by immunity, which is chronological age-dependent. We consider an age-structured epidemiological model that accounts for both passively acquired maternal antibodies that decay and active immunity that wanes, permitting reinfection. The model is a 6-dimensional system of partial differential equations (PDE). By assuming constant rates within each age-group, the PDE system can be reduced to an ordinary differential equation (ODE) system with aging from one age-group to the next. We derive formulae for the effective reproduction number ℛ and provide their biological interpretation in some special cases. We show that the disease-free equilibrium is stable when ℛ < 1 and unstable if ℛ > 1.
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Pubmed ID:29249910
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Pubmed Central ID:PMC5730097
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Volume:21
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Issue:2
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