A Filippov system describing media effects on the spread of infectious diseases

Nonlinear Analysis: Hybrid Systems

Volumn 11, Issue 1, 2014, Pages 84-97

  Wang, Aili ^a,b   Xiao, Yanni ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b BAOJI UNIVERSITY OF ARTS AND SCIENCES   (China)

Author keywords

Filippov system; Global asymptotic stability; Media coverage; Sliding bifurcation; Threshold policy

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS);

FILIPPOV SYSTEMS; GLOBAL ASYMPTOTIC STABILITY; MEDIA COVERAGE; SLIDING BIFURCATION; THRESHOLD POLICIES;

DISEASES;

EID: 84880793555     PISSN: 1751570X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nahs.2013.06.005     Document Type: Article

References (28)

1. Liu R.S., Wu J.H., Zhu H.P. Media/psychological impact on multiple outbreaks of emerging infectious diseases. Comput. Math. Methods Med. 2007, 8(3):153-164.
2. Tchuenche J.M., Dube N., Bhunu C.P., Smith R.J., Bauch C. The impact of media coverage on the transmission dynamics of human influenza. BMC Public Health 2011, 11(Suppl. 1):S5.
3. Cui J.A., Sun Y.H., Zhu H.P. The impact of media on the control of infectious diseases. J. Dynam. Differential Equations 2008, 20:31-53.
4. Cui J.A., Tao X., Zhu H.P. An SIS infection model incorporating media coverage. Rocky Mountain J. Math. 2008, 38(5):1323-1334.
5. Sun C.J., Yang W., Arino J., Khan K. Effect of media-induced social distancing on disease transmission in a two patch setting. Math. Biosci. 2011, 10.1016/j.mbs.2011.01.005.
6. Li Y.F., Cui J.A. The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage. Commun. Nonlinear Sci. Numer. Simul. 2009, 14:2353-2365.
7. Tang S.Y., Xiao Y.N., et al. Community-based measures for mitigating the 2009 H1N1 pandemic in China. PLoS One 2010, 5(6):e10911. 10.1371/journal.pone.0010911.
8. Cai L.M., Li X.Z. Analysis of a SEIV epidemic model with a nonlinear incidence rate. Appl. Math. Model. 2009, 33:2919-2926.
9. Maggie F. New flu has been around for years in pigs: study. Reuters: Science 2009, 11 June.
10. Hethcote H.W. Qualitative analyses of communicable disease models. Math. Biosci. 1976, 28:335-356.
11. Keeling M.J., Rohani P. Modeling Infectious Diseases in Human and Animals 2008, Princeton University Press, Princeton.
12. Filippov A.F. Differential Equations with Discontinuous Righthand Sides 1988, Kluwer Academic, Dordrecht.
13. Reppasa A.I., Tsoumanisb A.C., Siettos C.I. Coarse-grained bifurcation analysis and detection of criticalities of an individual-based epidemiological network model with infection control. Appl. Math. Model. 2010, 34:552-560.
14. Xiao Y.N., Zhou Y.C., Tang S.Y. Modelling disease spread in dispersal networks at two levels. IMA J. Math. Appl. Med. Biol. 2011, 28:227-244.
15. Sun S.L., Chen L.S. Mathematical modelling to control a pest population by infected pests. Appl. Math. Model. 2009, 33:2864-2873.
16. Corless R.M., Gonnet G.H., et al. On the Lambert W function. Adv. Comput. Math. 1996, 5:329-359.
17. Utkin V.I. Sliding Modes and their Applications in Variable Structure Systems 1978, Mir, Moscow.
18. Utkin V.I. Sliding Modes in Control and Optimization 1992, Springer, Berlin.
19. Kuznetsov Yu.A., Rinaldi S., Gragnani A. One parameter bifurcations in planar Filippov systems. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 2003, 13:2157-2188.
20. Bernardo M.D., Budd C.J., Champneys A.R., et al. Bifurcations in nonsmooth dynamical systems. SIAM Rev. 2008, 50:629-701.
21. Wang W.D. Backward bifurcation of an epidemic model with treatment. Math. Biosci. 2006, 201:58-71.
22. Xiao Y.N., Xu X.X., Tang S.Y. Sliding mode control of outbreaks of emerging infectious diseases. Bull. Math. Biol. 2012, 74:2403-2422.
23. Costa M.I.S., Kaszkurewicz E., Bhaya A., Hsu L. Achieving global convergence to an equilibrium population in predator-prey systems by the use of a discontinuous harvesting policy. Ecol. Model. 2000, 128:89-99.
24. M.E.M. Meza, M.I.S. Costa, A. Bhaya, E. Kaszkurewicz, Threshold policies in the control of predator-prey models, in: Preprints of the 15th Triennial World Congress, IFAC, Barcelona, Spain, 2002, pp. 1-6.
25. Tang S.Y., Liang J.H., Xiao Y.N., Cheke R.A. Sliding bifurcation of Filippov two stage pest control models with economic thresholds. SIAM J. Appl. Math. 2012, 72:1061-1080.
26. Tang S.Y., Liang J.H. Global qualitative analysis of a non-smooth Gause predator-prey model with a refuge. Nonlinear Analysis RWA 2013, 76:165-180.
27. Meza M.E.M., Bhaya A., Kaszkurewicz E.K., Silveira D.A., Costa M.I. Threshold policies control for predator-prey systems using a control Liapunov function approach. Theor. Popul. Biol. 2005, 67:273-284.
28. Boukal D.S., Krivan V. Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behavior. J. Math. Biol. 1999, 39:493-517.