A stochastic SIS epidemic model incorporating media coverage in a two patch setting

In this paper, we investigate the stochastic disease dynamics of an SIS epidemic model on two patches incorporating media coverage. We give the global existence and positivity of the solutions, and the sufficient conditions for almost surely exponentially stability of the disease-free equilibrium, which means that the disease will be stochastic extinction. Furthermore, we perform some numerical simulations to validate the analytical finding.

[1]  Yongli Cai,et al.  Spatiotemporal dynamics of a reaction–diffusion epidemic model with nonlinear incidence rate , 2011 .

[2]  F. Ball,et al.  Analysis of a stochastic SIR epidemic on a random network incorporating household structure. , 2010, Mathematical biosciences.

[3]  Zhenqing Li,et al.  Complex dynamics of a reaction–diffusion epidemic model , 2012 .

[4]  Daqing Jiang,et al.  Global stability of two-group SIR model with random perturbation☆ , 2009 .

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

[6]  Sanyi Tang,et al.  Dynamics of an infectious diseases with media/psychology induced non-smooth incidence. , 2013, Mathematical biosciences and engineering : MBE.

[7]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[8]  Jingan Cui,et al.  The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage , 2009 .

[9]  Anupama Sharma,et al.  Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases , 2011, Math. Comput. Model..

[10]  S. Zacks,et al.  Introduction to stochastic differential equations , 1988 .

[11]  Daqing Jiang,et al.  The long time behavior of DI SIR epidemic model with stochastic perturbation , 2010 .

[12]  Jing-An Cui,et al.  THE IMPACT OF MEDIA COVERAGE ON THE DYNAMICS OF INFECTIOUS DISEASE , 2008 .

[13]  P. Bonanni,et al.  Demographic impact of vaccination: a review. , 1999, Vaccine.

[14]  Huaiping Zhu,et al.  The Impact of Media on the Control of Infectious Diseases , 2007, Journal of dynamics and differential equations.

[15]  R M May,et al.  Harvesting Natural Populations in a Randomly Fluctuating Environment , 1977, Science.

[16]  L. Allen.  An Introduction to Stochastic Epidemic Models , 2008 .

[17]  Jiajia Yu,et al.  Asymptotic behavior of global positive solution to a stochastic SIR model , 2011, Math. Comput. Model..

[18]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[19]  Jean M. Tchuenche,et al.  Dynamics of an Infectious Disease Where Media Coverage Influences Transmission , 2012 .

[20]  Jianhua Pang,et al.  An SIRS Epidemiological Model with Nonlinear Incidence Rate Incorporating Media Coverage , 2009, 2009 Second International Conference on Information and Computing Science.

[21]  Sheri L. Bergeron,et al.  Media Effects on Students during SARS Outbreak , 2005, Emerging infectious diseases.

[22]  Zhen Jin,et al.  SPATIAL PATTERN IN AN EPIDEMIC SYSTEM WITH CROSS-DIFFUSION OF THE SUSCEPTIBLE , 2009 .

[23]  Tom Britton,et al.  Stochastic epidemic models: a survey. , 2009, Mathematical biosciences.

[24]  Huaiping Zhu,et al.  An SIS Infection Model Incorporating Media Coverage , 2008 .

[25]  R. Buchbinder,et al.  Surgery for treating femoroacetabular impingement , 2013 .

[26]  V. B. Kolmanovskii,et al.  Stability of epidemic model with time delays influenced by stochastic perturbations 1 This paper was , 1998 .

[27]  Yongli Cai,et al.  Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate , 2013 .

[28]  A. Sowden,et al.  Mass media interventions for preventing smoking in young people. , 1998, The Cochrane database of systematic reviews.

[29]  Zhen Jin,et al.  Analysis of Rabies in China: Transmission Dynamics and Control , 2011, PloS one.

[30]  Yongli Cai,et al.  Complex dynamics of a diffusive epidemic model with strong Allee effect , 2013 .

[31]  Kai Liu.  Stochastic Stability of Differential Equations in Abstract Spaces , 2019 .

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

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

[34]  Chris T Bauch,et al.  The impact of media coverage on the transmission dynamics of human influenza , 2011, BMC public health.

[35]  Julien Arino,et al.  Effect of media-induced social distancing on disease transmission in a two patch setting , 2011, Mathematical Biosciences.

[36]  Simon E. F. Spencer,et al.  Stochastic epidemic models for emerging diseases , 2008 .

[37]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[38]  Shigui Ruan,et al.  Global analysis of an epidemic model with nonmonotone incidence rate , 2006, Mathematical Biosciences.

[39]  F. Brauer,et al.  Mathematical Models in Population Biology and Epidemiology , 2001 .

[40]  Sebastian Walcher,et al.  Exclusion and persistence in deterministic and stochastic chemostat models , 2005 .

[41]  Philip K Maini,et al.  Non-linear incidence and stability of infectious disease models. , 2005, Mathematical medicine and biology : a journal of the IMA.

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

[43]  Zhien Ma,et al.  Modeling and dynamics of infectious diseases , 2009 .

[44]  Wenbin Liu,et al.  A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation , 2013 .

[45]  S. Aachen.  Stochastic Differential Equations An Introduction With Applications , 2016 .

[46]  Liangjian Hu,et al.  A Stochastic Differential Equation SIS Epidemic Model , 2011, SIAM J. Appl. Math..

[47]  X. Mao,et al.  Environmental Brownian noise suppresses explosions in population dynamics , 2002 .

[48]  S. Levin,et al.  Dynamical behavior of epidemiological models with nonlinear incidence rates , 1987, Journal of mathematical biology.