Global stability of two-scale network human epidemic dynamic model

Neural, Parallel and Scientific Computations

Volumn 19, Issue 1-2, 2011, Pages 65-90

  Wanduku, Divine ^a   Ladde, G S ^a  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Disease free steady state; Global asymptotic stability; Lypunov direct method; Lypunov function; Positively invariant set; Threshold value

Indexed keywords

EID: 80052891454     PISSN: 10615369     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

1. D. WANDUKU and G. S. Ladde (2010). A two-scale network dynamic model for human mobility process, Math. Biosci. Volume 229 (1) pages 1-15,
2. Patterson, K. D. (1986). Pandemic Influenza 1700-1900, Totowa, NJ: Rowman & Littlefield
3. van Hartesveldt, F. R. (Ed.) (1992a). Introduction, in The 1918-1919 Pandemic of Influenza: The Urban Impact in the Western World, Lewiston, NY: The Edwin Mellen Press, pp. 1-12.
4. Stacey Knobler, Adel Mahmoud, Stanley Lemon, and Leslie Pray (2006), The Impact of Globalization on Infectious Disease Emergence and Control: Exploring the Consequences and Opportunities, Workshop Summary - Forum on Microbial Threats, Washington D.C: The National Acedemies Press.
5. L. Rvachev and I. Longini, A mathematical model for the global spread of influenza, Math Biosci 75 (1985), pp. 3-22.
6. I. Longini, A mathematical model for predicting the geographic spread of new infectious agents, Math Biosci 90 (1988), pp. 367-383.
7. W. Wang and G. Mulone, Threshold of disease transmission in a patch environment, J Math Anal Appl 285 (2003), pp. 321-335.
8. W. Wang and X.-Q. Zhao, An epidemic model in a patchy environment, Math Biosci 190 (2004), pp. 97-112.
9. W. Wang and X.-Q. Zhao, An age-structured epidemic model in a patchy environment, SIAM J Appl Math 65 (2005), pp. 1597-1614.
10. C. Cosner, J. C. Beier, R.S.Cantrell, D. Impoinvil, L. Kapitanski, M. D. Potts, A.Troyo, and S. Ruan (2009), The effects of human movement on the persistence of vector borne diseases, Journal of Theoretical Biology Vol. 258, 550-560.
11. J. Arino and P. Van den Driessche, A multi-city epidemic model, Math Popul Stud 10 (2003), pp. 175-193.
12. J. Arino, J. R. Davis, D. Hartley, R. Jordan, J. M. Miller and P. van den Driessche, A multispecies epidemic model with spatial dynamics, Mathematical Medicine and Biology 22 (2005), pp. 129-142
13. Watts DJ, Muhamad R, Medina DC, and Dodds PS. 2005. Multiscale, resurgent epidemics in a hierarchical metapopulation model. Proceedings of the National Academy of Sciences, USA 102: 11157-11162. (Pubitemid 41153791)
14. Sattenspiel, L., and Dietz, K., 1995. A structured epidemic model incorporating geographic mobility among regions. Mathematical Biosciences 128, 7191
15. L. Sattenspiel and D. A. Herring, Structured epidemic models and the spread of influenza in the central Canada subarctic, Human Biol 70 (1998), pp. 91-115
16. L. Sattenspiel and D. A. Herring, Simulating the effect of quarantine on the spread of the 1918-1919 flu in central Canada, Bull Math Biol 65 (2003), pp. 1-26.
17. G. S. Ladde, Cellular Systems-II. Stability of Compartmental Systems, Math. Biosci. 30 (1976), 1-21
18. G. S. Ladde, Cellular Systems-I. Stability of Chemical Systems, Math Biosci. 29 (3/4) (1976), 309-330
19. G. S. Ladde, Competitive Processes and Comparison Differential Systems, Trans, of American Mathematical Society, 221 (1976), 391-402
20. Haber MJ, Shay DK, Davis XM, Patel R, Jin X, Weintraub E., Effectiveness of interventions to reduce contact rates during a simulated influenza pandemic. Emerg Infect Dis. (2007), vol. 13 (4).
21. CIA World Factbook, http://www.indexmundi.com/g/g.aspx?c=dr&v=25
22. CIA World Factbook, https://www.cia.gov/library/publications/the-world- factbook/rankorder/2102rank.html
23. 2009 H1N1 Flu: International Situation Update http://www.cdc.gov/h1n1flu/ updates/international/
24. B. Buonomo, and S. Rionero: On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate, Applied Mathematics and Computation, Volume 217, Issue 8, 15 December 2010, Pages 4010-1016
25. Jianhua Pang, and Jing-an Cui, "An SIRS Epidemiological Model with Nonlinear Incidence Rate Incorporating Media Coverage," icic, vol. 3, pp.116-119, 2009 Second International Conference on Information and Computing Science, 2009
26. Y. Jin, W. Wang and S. Xiao, An SIRS model with a nonlinear incidence rate, Chaos, Solitons Fractals 34 (2007), pp. 1482-1497.
27. A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol. 30 (2006), pp. 615-626.
28. A. Korobeinikov, Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol. 69 (2007), pp. 1871-1886
29. Zhixing Hu,Ping Bi, Wanbiao Ma, and Shigui Ruan: Bifurcations of an SIRS Epidemic Model with nonlinear incidence rate, Discrete And Continuous Dynamical Systems Series B, Volume 15, Number 1, January 2011, pp. 93-112
30. Bifurcation Analysis of an SIRS Epidemic Model with Generalized Incidence M. E. Alexander and S. M. Moghadas SIAM Journal on Applied Mathematics Vol. 65, No. 5 (May - Jul., 2005), pp. 1794-1816
31. Fuzhong Nian and Xingyuan Wang,Efficient immunization strategies on complex networks, Journal of Theoretical Biology, Volume 264, Issue 1, 7 May 2010, Pages 77-83
32. W. Tan and X. Zhu, A stochastic model for the HIV epidemic in homosexual populations involving age and race, Math. Comput. Modelling 24 (1996), pp. 67-105.
33. W. Tan and X. Zhu, A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes: I. The probabilities of HIV transmission and pair formation, Math. Comput. Modelling 24 (1996), pp. 47-107.
34. Nirav Dalala, David Greenhalgh, Xuerong Mao, A stochastic model of AIDS and condom use, Journal of Mathematical Analysis and Applications Volume 325, Issue 1, 1 January 2007, Pages 36-53
35. Nirav Dalal, David Greenhalgh, and Xuerong Mao, A stochastic model for internal HIV dynamics Original Research Article Journal of Mathematical Analysis and Applications, Volume 341, Issue 2, 15 May 2008, Pages 1084-1101
36. Z. Jin, Z. Ma and M. Han, Global stability of an SIRS epidemic model with delays, Acta Math. Sci. 26 (2006), pp. 291-306.
37. Ruan et al., 2006 S. Ruan, W. Wang and S.A. Levin, The effect of global travel on the spread of SARS, Mathematical Biosciences and Engineering 3 (2006), pp. 205-218.
38. Rodriguez and Torres-Sorando, 2001 D.J. Rodriguez and L. Torres-Sorando, Models for infectious diseases in spatially heterogeneous environments, Bulletin of Mathematical Biology 63 (2001), pp. 547-571.
39. J. Yu, D. Jiang and N. Shi, Global stability of two-group SIR model with random perturbation, J. Math. Anal. Appl. 360 (2009), pp. 235-244.
40. E. Tornatore, S.M. Buccellato and P. Vetro, Stability of a stochastic SIR system, Phys. A 354 (2005), pp. 111-126.
41. Zhen jin, Ma zhien, Han Maoan, Global Stability of an SIRS epidemic model with delays, Acta Mathematica Scientia, 26B, 291-306, 2006.
42. Junjie Chen: An SIRS epidemic model ,Applied Mathematics - A Journal of Chinese Universities(2004), Volume 19, Number 1, 101-108
43. G. S. Ladde, V. Lakshmikantham, Random Differential Inequalities, Academic press, New York, 1980
44. W. Walter, Ordinary Differential Equations, Springer-Verlag, 1998, vol.182
45. R. M. Murray, Z. Li and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation. CRC Press, 1993.
46. X. Liao, L.Q. Wang, P.Yu, Stability of Dynamical Systems, Elsevier, 2007
47. Uri M. Ascher, Linda, R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-algebraic Equations, siam 1998