caa a22 4500 445330236 CHVBK 20180317142734.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00285-010-0327-y doi (NATIONALLICENCE)springer-10.1007/s00285-010-0327-y Stability of differential susceptibility and infectivity epidemic models [Elektronische Daten] [B. Bonzi, A. Fall, A. Iggidr, G. Sallet] We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio $${\mathcal{R}_0 \leq 1}$$ and the existence and uniqueness of an endemic equilibrium when $${\mathcal{R}_0 >1 }$$ . We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when $${\mathcal{R}_0 >1 }$$ . Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626-644, 2005; Math Biosci Eng 3:89-100, 2006). Springer-Verlag, 2010 Nonlinear dynamical systems nationallicence Global stability nationallicence Lyapunov methods nationallicence Differential susceptibility models nationallicence Reproductive number nationallicence HBV nationallicence Bonzi B. Université de Ouagadougou, UFR SEA, Ouagadougou, Burkina Faso aut Fall A. MASAIE Team, INRIA-Nancy Grand Est, Université Paul Verlaine, Metz, LMAM (UMR CNRS 7122), ISGMP Bât A, Ile du Saulcy, 57045, Metz Cedex 01, France aut Iggidr A. MASAIE Team, INRIA-Nancy Grand Est, Université Paul Verlaine, Metz, LMAM (UMR CNRS 7122), ISGMP Bât A, Ile du Saulcy, 57045, Metz Cedex 01, France aut Sallet G. MASAIE Team, INRIA-Nancy Grand Est, Université Paul Verlaine, Metz, LMAM (UMR CNRS 7122), ISGMP Bât A, Ile du Saulcy, 57045, Metz Cedex 01, France aut Journal of Mathematical Biology Springer-Verlag 62/1(2011-01-01), 39-64 0303-6812 62:1<39 2011 62 285 https://doi.org/10.1007/s00285-010-0327-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0327-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bonzi B. Université de Ouagadougou, UFR SEA, Ouagadougou, Burkina Faso aut NATIONALLICENCE 700 1- Fall A. MASAIE Team, INRIA-Nancy Grand Est, Université Paul Verlaine, Metz, LMAM (UMR CNRS 7122), ISGMP Bât A, Ile du Saulcy, 57045, Metz Cedex 01, France aut NATIONALLICENCE 700 1- Iggidr A. MASAIE Team, INRIA-Nancy Grand Est, Université Paul Verlaine, Metz, LMAM (UMR CNRS 7122), ISGMP Bât A, Ile du Saulcy, 57045, Metz Cedex 01, France aut NATIONALLICENCE 700 1- Sallet G. MASAIE Team, INRIA-Nancy Grand Est, Université Paul Verlaine, Metz, LMAM (UMR CNRS 7122), ISGMP Bât A, Ile du Saulcy, 57045, Metz Cedex 01, France aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 62/1(2011-01-01), 39-64 0303-6812 62:1<39 2011 62 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer