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The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by generation expansion (with the generation number corresponding to the number of times an individual became infected).
In joint work in progress with Wilfred de Graaf, Peter Teunis and Mirjam Kretzschmar we want to use either the generation expansion or an invariant/stable distribution as the starting point for the efficient computation of coarse statistics. The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by ...

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Documents 45D05 | enregistrements trouvés : 45

Boosting and waning: on the dynamics of immune status Diekmann, Odo | CIRM H Nouveau

Seminar on differential equations and dynamical systems II Yorke, J. A. | Springer-Verlag 1970 Nouveau

Fractional calculus and its applicationsproceedings of the international conferenceJune 15-16 Ross, Bertram | Springer-Verlag 1975 Nouveau

Volterra equations :proceedings of the helsinki symposium on integral equations#Aug. 11-14 Londen, Stig-Olof ; Staffans, Olof J. | Springer-Verlag 1979 Nouveau

Trends in the theory and practice of non-linear analysisproceedings of the vith international conference on... held at the university of texas at arlington,june 18-22, 1984 Lakshmikantham, V. | North-Holland 1985 Nouveau

Constructive methods for the practical treatment of integtal equationsproceedings of the conference at the mathematisches forschungsinstitut,oberwol fach,june 24-30,1984 Hammerlin, G. ; Hoffmann, K. H. | Birkhäuser Verlag 1985 Nouveau

Treatment of integral equation by numerical methodsbased on the proceedings of a symposium held in Durham,19-29 july,1982, organized under the auspice of the l.m. s. Baker, Christopher T. H. ; Miller, Geoffrey F. | Academic Press 1982 Nouveau

Theory of functionals and of integral and integro-differential equations Volterra, Vito | Dover Publications 1959 Nouveau

Trudy po topologii i drugim oblastyam matematiki [Difficultés en topologie et travaux mathématiques] Urysson, P.S. | Etat de Litterature Technico-Théorique 1951 Nouveau

Integral equations Tricomi, F. G. | John Wiley And Sons 1957 Nouveau

Volterra adventures Shapiro, Joel H. | American Mathematical Society 2018 Nouveau

Evolutionary integral equation and applications Prüss, Jan | Birkhäuser Verlag 1993 Nouveau

Integral equations and their applications Vol. I Pogorzelski, W. | PWN-Polish Scientific Publishers;Pergamon Press 1966 Nouveau

Applications physiques de la transformation de Laplace. Vol. I :méthodes de calcul Parodi, Maurice ; Pérès, Joseph | CNRS 1948 Nouveau

Two papers on similarity of certain Volterra integral operators Osher, Stanley J. | American Mathematical Society 1967 Nouveau

Non-oscillation domains of differential equations with two parameters Mingarelli, Angelo B. ; Halvorsen, S. Gotskalk | Springer-Verlag 1988 Nouveau

Volterra-Stieltjes integral equations and generalized ordinary differential expressions Mingarelli, Angelo B. | Springer-Verlag 1983 Nouveau

Volterra integral equations and topological dynamics Miller, Richard K. ; Sell, George R. | American Mathematical Society 1970 Nouveau

Nonlinear Volterra integral equations Miller, Richard K. | W. A. Benjamin Inc. 1971 Nouveau

Le calcul différentiel dans les espaces de Banach. Vol. 1 :fonctions analytiques - équations intégrales Michal, Aristotle D. ; Frechet, Maurice ; Mourier, E. | Gauthier-Villars 1958 Nouveau

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Fractional calculus and its applications
proceedings of the international conference
June 15-16 Ross, Bertram | Springer-Verlag 1975 Nouveau

Volterra equations :
proceedings of the helsinki symposium on integral equations#Aug. 11-14 Londen, Stig-Olof ; Staffans, Olof J. | Springer-Verlag 1979 Nouveau

Trends in the theory and practice of non-linear analysis
proceedings of the vith international conference on... held at the university of texas at arlington,june 18-22, 1984 Lakshmikantham, V. | North-Holland 1985 Nouveau

Constructive methods for the practical treatment of integtal equations
proceedings of the conference at the mathematisches forschungsinstitut,oberwol fach,june 24-30,1984 Hammerlin, G. ; Hoffmann, K. H. | Birkhäuser Verlag 1985 Nouveau

Treatment of integral equation by numerical methods
based on the proceedings of a symposium held in Durham,19-29 july,1982, organized under the auspice of the l.m. s. Baker, Christopher T. H. ; Miller, Geoffrey F. | Academic Press 1982 Nouveau

Applications physiques de la transformation de Laplace. Vol. I :
méthodes de calcul Parodi, Maurice ; Pérès, Joseph | CNRS 1948 Nouveau

Le calcul différentiel dans les espaces de Banach. Vol. 1 :
fonctions analytiques - équations intégrales Michal, Aristotle D. ; Frechet, Maurice ; Mourier, E. | Gauthier-Villars 1958 Nouveau