MIXED VACCINATION STRATEGY IN SIRS EPIDEMIC MODEL WITH SEASONAL VARIABILITY ON INFECTION

In many diseases seasonal fluctuations are observed. SIRS epidemic model with seasonal varying contact rate and mixed vaccination strategy (including first vaccination and pulse vaccination strategy) is investigated. The effects of the variation of dependent on the season of the contact rate and the vaccination strategy to eradicate infectious diseases are studied and discussed. A threshold for a disease to be extinct or endemic is established. The existence and global asymptotic stability of disease-free periodic solution and the permanence of the disease are illustrated. Finally, our theoretical results are confirmed by numerical simulations.

[1]  Lansun Chen,et al.  The dynamics of an epidemic model for pest control with impulsive effect , 2010 .

[2]  G. Serio,et al.  A generalization of the Kermack-McKendrick deterministic epidemic model☆ , 1978 .

[3]  Zhidong Teng,et al.  Analysis of an SEIRS Epidemic Model with Time Delays And Pulse Vaccination , 2008 .

[4]  R. Anderson,et al.  Pulse mass measles vaccination across age cohorts. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[5]  J. Gonzalez,et al.  Dengue hemorrhagic fever epidemiology in Thailand: description and forecasting of epidemics. , 2002, Microbes and infection.

[6]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[7]  Alberto d'Onofrio,et al.  Stability properties of pulse vaccination strategy in SEIR epidemic model. , 2002, Mathematical biosciences.

[8]  I B Schwartz,et al.  Small amplitude, long period outbreaks in seasonally driven epidemics , 1992, Journal of mathematical biology.

[9]  J. Yorke,et al.  Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. , 1973, American journal of epidemiology.

[10]  Alberto d'Onofrio,et al.  Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times , 2004, Appl. Math. Comput..

[11]  Guirong Jiang,et al.  Bifurcation analysis in an SIR epidemic model with birth pulse and pulse vaccination , 2009, Appl. Math. Comput..

[12]  Xuebin Chi,et al.  The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission , 2002 .

[13]  J. Dushoff,et al.  Dynamical resonance can account for seasonality of influenza epidemics. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[14]  I B Schwartz,et al.  Seasonality and period-doubling bifurcations in an epidemic model. , 1984, Journal of theoretical biology.

[15]  Shujing Gao,et al.  Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. , 2006, Vaccine.

[16]  Zvia Agur,et al.  Theoretical examination of the pulse vaccination policy in the SIR epidemic model , 2000 .

[17]  Y. Iwasa,et al.  Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models , 1986, Journal of mathematical biology.

[18]  Lansun Chen,et al.  TWO DIFFERENT VACCINATION STRATEGIES IN AN SIR EPIDEMIC MODEL WITH SATURATED INFECTIOUS FORCE , 2008 .

[19]  Lansun Chen,et al.  A delayed epidemic model with stage-structure and pulses for pest management strategy , 2008 .

[20]  Q. J. A. Khan,et al.  Hopf bifurcation in two SIRS density dependent epidemic models , 2004 .

[21]  Zhen Jin,et al.  Pulse vaccination in the periodic infection rate SIR epidemic model , 2008 .

[22]  I. Kleinschmidt,et al.  Exploring 30 years of malaria case data in KwaZulu‐Natal, South Africa: Part I. The impact of climatic factors , 2004, Tropical medicine & international health : TM & IH.

[23]  Xianning Liu,et al.  SVIR epidemic models with vaccination strategies. , 2008, Journal of theoretical biology.

[24]  P. van den Driessche,et al.  Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population , 2003 .

[25]  A. J. Hall.  Infectious diseases of humans: R. M. Anderson & R. M. May. Oxford etc.: Oxford University Press, 1991. viii + 757 pp. Price £50. ISBN 0-19-854599-1 , 1992 .

[26]  M R Al-Ajam,et al.  Mucormycosis in the Eastern Mediterranean: a seasonal disease , 2005, Epidemiology and Infection.

[27]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[28]  Zhen Jin,et al.  Analysis of a Delayed SIR Model with Nonlinear Incidence Rate , 2008 .

[29]  Zhenqing Li,et al.  Dynamics of a novel nonlinear SIR model with double epidemic hypothesis and impulsive effects , 2009, Nonlinear dynamics.

[30]  H. Hethcote.  Qualitative analyses of communicable disease models , 1976 .

[31]  James A. Yorke,et al.  Some equations modelling growth processes and gonorrhea epidemics , 1973 .

[32]  K. Dietz,et al.  The Incidence of Infectious Diseases under the Influence of Seasonal Fluctuations , 1976 .

[33]  James Watmough,et al.  A simple SIS epidemic model with a backward bifurcation , 2000, Journal of mathematical biology.

[34]  H. Thieme,et al.  Recurrent outbreaks of childhood diseases revisited: the impact of isolation. , 1995, Mathematical biosciences.

[35]  Xianning Liu,et al.  Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment , 2009 .

[36]  I. A. Moneim,et al.  The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study , 2007, Comput. Biol. Medicine.

[37]  J. Velasco-Hernández,et al.  A simple vaccination model with multiple endemic states. , 2000, Mathematical biosciences.

[38]  S. Levin.  Lectu re Notes in Biomathematics , 1983 .

[39]  Shigui Ruan,et al.  Dynamical behavior of an epidemic model with a nonlinear incidence rate , 2003 .

[40]  Jonathan Dushoff,et al.  Ecology and evolution of the flu , 2002 .