Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model

Journal of Applied Mathematics and Computing - Tập 41 Số 1-2 - Trang 99-117 - 2013
Junyuan Yang1,2, Yuming Chen1,2, Fengqin Zhang1
1Department of Applied Mathematics, Yuncheng University, Yuncheng, P.R. China
2Department of Mathematics, Wilfrid Laurier University, Waterloo, Canada

Tóm tắt

Từ khóa


Tài liệu tham khảo

Blayneh, K.W., Gumel, A.B., Lenhart, S., Clayton, T.: Backward bifurcation and optimal control in transmission dynamics of West Nile virus. Bull. Math. Biol. 72, 1006–1028 (2010)

Chinese Ministry of Health: http://www.moh.gov.cn/publicfiles/business/htmlfiles/zwgkzt/pyq/index.htm

Chuo, F., Tiing, S., Labadin, J.: A simple deterministic model for the spread of hand, foot and mouth disease (HFMD) in Sarawak. In: 2008 Second Asia International Conference on Modelling and Simulation, pp. 947–952

Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J.: On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990)

Fleming, W.H., Rishel, R.W.: Deterministic and Stochastic Optimal Control. Springer, New York (1975)

Hii, Y.L., Rocklöv, J., Ng, N.: Short term effects of weather on hand, foot and mouth disease. PLoS ONE 6(2), e16796 (2011)

Hirsch, W.M., Hanisch, H., Gabriel, J.-P.: Differential equation models of some parasitic infections: methods for the study of asymptotic behaviour. Commun. Pure Appl. Math. 38, 733–753 (1985)

Kar, T.K., Batabyal, A.: Stability analysis and optimal control of an SIR epidemic model with vaccination. Biosystems 104, 127–135 (2011)

Knipl, D.H., Röst, G.: Modelling the strategies for age specific vaccination scheduling during influenza pandemic outbreaks. Math. Biosci. Eng. 8(1), 123–139 (2011)

LaSalle, J.P.: The Stability of Dynamical Systems. SIAM, Philadelphia (1976)

Lee, S., Chowell, G., Castillo-Chávez, C.: Optimal control for pandemic influenza: the role of limited antiviral treatment and isolation. J. Theor. Biol. 265(2), 136–150 (2010)

Lee, S., Golinski, M., Chowell, G.: Modeling optimal age-specific vaccination strategies against pandemic influenza. Bull. Math. Biol. 74(4), 958–980 (2012)

Lenhart, S., Workman, J.T.: Optimal Control Applied to Biological Models. Chapman & Hall/CRC, London (2007)

Leong, P.F., Labadin, J., Rahman, S.B.A., Juan, S.F.S.: Quantifying the relationship between the climate and hand-foot-mouth disease (HFMD) incidences. In: 4th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), pp. 1–5 (2011)

Liu, J.: Threshold dynamics for a HFMD epidemic model with periodic transmission rate. Nonlinear Dyn. 64, 89–95 (2011)

Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: The Mathematical Theory of Optimal Processes. Gordon & Breach, New York (1986)

Prosper, O., Saucedo, O., Thompson, D., Torres-Garcia, G., Wang, X., Castillo-Chavez, C.: Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Math. Biosci. Eng. 8, 141–170 (2011)

Roy, N., Halder, N.: Compartmental modeling of hand, foot and mouth infectious disease (HFMD). Res. J. Appl. Sci. 5, 177–182 (2010)

The People’s Republic of China Yearbook 2009, English edn. China Yearbook Press, Beijing (2010)

The People’s Republic of China Yearbook 2010, English edn. China Yearbook Press, Beijing (2011)

Thieme, H.R.: Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24, 407–435 (1993)

Urashima, M., Shindo, N., Okabe, N.: Seasonal models of herpangina and hand-foot-mouth disease to simulate annual fluctuations in urban warming in Tokyo. Jpn. J. Infect. Dis. 56, 48–53 (2003)

van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)

Wang, J.-f., Guo, Y.-S., Christakos, G., Yang, W.-Z., Liao, Y.-L., Li, Z.J., Li, X.-Z., Lai, S.-J., Chen, H.-Y.: Hand, foot and mouth disease: spatiotemporal transmission and climate. Int. J. Health Geogr. 10, 25 (2011) (10 pages)

Zaman, G., Kang, Y.H., Jung, I.H.: Stability analysis and optimal vaccination of an SIR epidemic model. Biosystems 93, 240–249 (2008)

Zhu, Q., Hao, Y.T., Ma, J.Q., Yu, S.C., Wang, Y.: Surveillance of hand, foot, and mouth disease in Mainland China (2008–2009). Biomed. Environ. Sci. 24, 349–356 (2011)