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日時: 2016年10月5日(水) 15:30-16:30
会場: 数理科学研究科棟(駒場) 002号室
Odo Diekmann 氏 (Utrecht University)
Waning and boosting : on the dynamics of immune status (ENGLISH)
A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there. [1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388 [2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259 [3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7 [4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47