`a`
Mathematical Biosciences and Engineering (MBE)
 

Impact of discontinuous treatments on disease dynamics in an SIR epidemic model
Pages: 97 - 110, Issue 1, January 2012

doi:10.3934/mbe.2012.9.97      Abstract        References        Full text (382.0K)           Related Articles

Zhenyuan Guo - College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China (email)
Lihong Huang - College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China (email)
Xingfu Zou - Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada (email)

1 M. E. Alexander, C. Bowman, S. M. Moghadas, R. Summers, A. B. Gumel and B. M. Sahai, A vaccination model for transmission dynamics of influenza, SIAM J. Appl. Dyn. Syst., 3 (2004), 503-524.       
2 M. E. Alexander, S. M. Moghadas, P. Rohani and A. R. Summers, Modelling the effect of a booster vaccination on disease epidemiology, J. Math. Biol., 52 (2006), 290-306.       
3 M. E. Alexander, S. M. Moghadas, G. Röst and J. Wu, A delay differential model for pandemic influenza with antiviral treatment, Bull. Math. Biol., 70 (2008), 382-397.       
4 R. M. Anderson and R. M. May, "Infectious Diseases of Humans, Dynamics and Control," Oxford University, Oxford, 1991.
5 J. Arino, C. McCluskey and P. van den Driessche, Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J. Appl. Math., 64 (2003), 260-276.       
6 J. Arino, R. Jordan and P. van den Driessche, Quarantine in a multi-species epidemic model with spatial dynamics, Math. Biosci., 206 (2007), 46-60.       
7 J.-P. Aubin and A. Cellina, "Differential Inclusions. Set-Valued Maps and Viability Theory," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 264, Springer-Verlag, Berlin, 1984.       
8 A. Baciotti and F. Ceragioli, Stability and stabilization of discontinuous systems and nonsmooth Lyapunov function, ESAIM Control Optim. Calc. Var., 4 (1999), 361-376.       
9 F. Brauer, Backward bifurcations in simple vaccination models, J. Math. Anal. Appl., 298 (2004), 418-431.       
10 F. Brauer, Epidemic models with heterogeneous mixing and treatment, Bull. Math. Biol., 70 (2008), 1869-1885.       
11 F. Brauer, P. van den Driessche and J. Wu, eds., "Mathematical Epidemiology," Lecture Notes in Mathematics, 1945, Mathematical Biosciences Subseries, Springer-Verlag, Berlin, 2008.       
12 C. Castillo-Chavez and Z. Feng, To treat or not to treat: The case of tuberculosis, J. Math. Biol., 35 (1997), 629-656.       
13 F. Ceragioli, "Discontinuous Ordinary Differential Equations and Stabilization," Universita di Firenze, 2000.
14 F. H. Clarke, "Optimization and Non-Smooth Analysis," Wiley, New York, 1983.
15 Z. Feng, Final and peak epidemic sizes for SEIR models with quarantine and isolation, Math. Biosci. Eng., 4 (2007), 675-686.       
16 Z. Feng and H. R. Thieme, Recurrent outbreaks of childhood diseases revisited: The impact of isolation, Math. Biosci., 128 (1995), 93-130.       
17 A. F. Filippov, "Differential Equations with Discontinuous Righthand Sides," Translated from the Russian, Mathematics and its Applications (Soviet Series), 18, Kluwer Academic Publishers Group, Dordrecht, 1988.       
18 M. Forti, M. Grazzini, P. Nistri and L. Pancioni, Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations, Phys. D, 214 (2006), 88-99.       
19 J. M. Hyman and J. Li, Modeling the effectiveness of isolation strategies in preventing STD epidemics, SIAM J. Appl. Math., 58 (1998), 912-925.       
20 M. Nuño, Z. Feng, M. Martcheva and C. Castillo-Chavez, Dynamics of two-strain influenza with isolation and partial cross-immunity, SIAM J. Appl. Math., 65 (2005), 964-982.       
21 W. Wang, Backward bifurcation of an epidemic model with treatment, Math. Biosci., 201 (2006), 58-71.       
22 L. Wu and Z. Feng, Homoclinic bifurcation in an SIQR model for childhood diseases, J. Differ. Equat., 168 (2000), 150-167.       
23 X. Zhang and X. Liu, Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment, Nonl. Anal. RWA, 10 (2009), 565-575.       

Go to top