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A mathematical model of the PurkinjeMuscle Junctions
An SEIR epidemic model with constant latency time and infectious period
1.  CIMAB, University of Milano, via C. Saldini 50, I20133 Milano, Italy 
2.  Department of Mathematics and Computer Science, University of Udine, via delle Scienze 206, I33100 Udine, Italy 
References:
[1] 
E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 11441165. 
[2] 
V. Capasso and G. Serio, A generalization of the KermackMcKendric deterministic epidemic model, Math. Biosci., 42 (1978), 4361. doi: 10.1016/00255564(78)900068. 
[3] 
M. Giaquinta and G. Modica, "Mathematical Analysis. An Introduction to Functions of Several Variables," Birkhauser Boston, Inc., Boston, MA, 2009. 
[4] 
G. Huang and Y. Takeuchi, Global analysis on delay epidemiological dynamic models with nonlinear incidence, J. Math. Biol., 63 (2011), 125139. 
[5] 
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infection, SIAM J. Appl. Math., 70 (2010), 26932708. doi: 10.1137/090780821. 
[6] 
G. Huang, Y. Takeuchi, W. Ma and D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 11921207. doi: 10.1007/s1153800994876. 
[7] 
A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 18711886. doi: 10.1007/s115380079196y. 
[8] 
Y. Kuang, "Delay Differential Equations with Application in Population Dynamics," Dynamics in Science and Engineering, Academic Press, New York, 1993. 
[9] 
M. A. Safi and A. B. Gumel, Global asymptotic dynamics of a model of quarantine and isolation, Discrete Contin. Dyn. S., 14 (2010), 209231. doi: 10.3934/dcdsb.2010.14.209. 
[10] 
H. L. Smith, "An Introduction to Delay Differential Equations with Applications to the Life Sciences," Texts in Applied Mathematics, Springer, New York, 2011. doi: 10.1007/9781441976468. 
[11] 
R. Xu and Y. Du, \ A delayed SIR epidemic model with saturation incidence and constant infectious period, J. Appl. Math. Comp., 35 (2010), 229250. doi: 10.1007/s1219000903533. 
[12] 
R. Xu and Z. Ma, Global stability of a delayed SEIRS epidemic model with saturation incidence rate, Nonlinear Dynam., 61 (2010), 229239. doi: 10.1007/s1107100996443. 
[13] 
F. Zhang, Z. Li and F. Zhang, Global stability of an SIR epidemic model with constant infectious period, Appl. Math. Comput, 199 (2008), 285291. doi: 10.1016/j.amc.2007.09.053. 
show all references
References:
[1] 
E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 33 (2002), 11441165. 
[2] 
V. Capasso and G. Serio, A generalization of the KermackMcKendric deterministic epidemic model, Math. Biosci., 42 (1978), 4361. doi: 10.1016/00255564(78)900068. 
[3] 
M. Giaquinta and G. Modica, "Mathematical Analysis. An Introduction to Functions of Several Variables," Birkhauser Boston, Inc., Boston, MA, 2009. 
[4] 
G. Huang and Y. Takeuchi, Global analysis on delay epidemiological dynamic models with nonlinear incidence, J. Math. Biol., 63 (2011), 125139. 
[5] 
G. Huang, Y. Takeuchi and W. Ma, Lyapunov functionals for delay differential equations model of viral infection, SIAM J. Appl. Math., 70 (2010), 26932708. doi: 10.1137/090780821. 
[6] 
G. Huang, Y. Takeuchi, W. Ma and D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 11921207. doi: 10.1007/s1153800994876. 
[7] 
A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 18711886. doi: 10.1007/s115380079196y. 
[8] 
Y. Kuang, "Delay Differential Equations with Application in Population Dynamics," Dynamics in Science and Engineering, Academic Press, New York, 1993. 
[9] 
M. A. Safi and A. B. Gumel, Global asymptotic dynamics of a model of quarantine and isolation, Discrete Contin. Dyn. S., 14 (2010), 209231. doi: 10.3934/dcdsb.2010.14.209. 
[10] 
H. L. Smith, "An Introduction to Delay Differential Equations with Applications to the Life Sciences," Texts in Applied Mathematics, Springer, New York, 2011. doi: 10.1007/9781441976468. 
[11] 
R. Xu and Y. Du, \ A delayed SIR epidemic model with saturation incidence and constant infectious period, J. Appl. Math. Comp., 35 (2010), 229250. doi: 10.1007/s1219000903533. 
[12] 
R. Xu and Z. Ma, Global stability of a delayed SEIRS epidemic model with saturation incidence rate, Nonlinear Dynam., 61 (2010), 229239. doi: 10.1007/s1107100996443. 
[13] 
F. Zhang, Z. Li and F. Zhang, Global stability of an SIR epidemic model with constant infectious period, Appl. Math. Comput, 199 (2008), 285291. doi: 10.1016/j.amc.2007.09.053. 
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