Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity

Abstract An autonomous deterministic non-linear epidemic model SEQIHRS is proposed for the transmission dynamics of an infectious disease with quarantine and isolation control strategies in a community with pre-existing immunity. The model exhibits two equilibria, namely, the disease-free and a unique endemic equilibrium. The existence and local stability of the disease free and endemic equilibria are explored in terms of the effective reproduction number R C . It is observed that media coverage does not affect the effective reproduction number, but it helps to mitigate disease burden by lowering the number of infectious individuals at the endemic steady state and also lowering the infection peak. A new approach is proposed to estimate the coefficient of media coverage. Using the results of central manifold theory, it is established that as R C passes through unity, transcritical bifurcation occurs in the system and the unique endemic equilibrium is asymptotically stable. It is observed that the population level impact of quarantine and isolation depend on the level of transmission by the isolated individuals. Moreover, the higher level of pre-existing immunity in the population decreases the infection peak and causes its early arrival. Theoretical findings are supported by numerical simulation. Sensitivity analysis is performed for R C and state variables at endemic steady state with respect to model parameters.

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

[2]  Deborah Lacitignola,et al.  Global stability of an SIR epidemic model with information dependent vaccination. , 2008, Mathematical biosciences.

[3]  Abba B. Gumel,et al.  The effect of incidence functions on the dynamics of a quarantine/isolation model with time delay , 2010, Nonlinear Analysis: Real World Applications.

[4]  C. Watkins,et al.  The spread of awareness and its impact on epidemic outbreaks , 2009, Proceedings of the National Academy of Sciences.

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

[6]  Robert J. Smith,et al.  Assessing the impact of educational campaigns on controlling HCV among women in prison settings , 2011 .

[7]  Troy Day,et al.  When Is Quarantine a Useful Control Strategy for Emerging Infectious Diseases? , 2006, American journal of epidemiology.

[8]  J. Robins,et al.  Transmission Dynamics and Control of Severe Acute Respiratory Syndrome , 2003, Science.

[9]  Carlos Castillo-Chavez,et al.  Dynamics of Two-Strain Influenza with Isolation and Partial Cross-Immunity , 2005, SIAM J. Appl. Math..

[10]  Shigui Ruan,et al.  Uniform persistence and flows near a closed positively invariant set , 1994 .

[11]  James M. Hyman,et al.  Mathematical Modeling of the Effectiveness of Facemasks in Reducing the Spread of Novel Influenza A (H1N1) , 2010, PloS one.

[12]  H. Hethcote,et al.  Effects of quarantine in six endemic models for infectious diseases. , 2002, Mathematical biosciences.

[13]  Md. Samsuzzoha,et al.  Uncertainty and sensitivity analysis of the basic reproduction number of a vaccinated epidemic model of influenza , 2013 .

[14]  Rahul Raman,et al.  Structural Determinants for Naturally Evolving H5N1 Hemagglutinin to Switch Its Receptor Specificity , 2013, Cell.

[15]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[16]  A. Sharma,et al.  The role of the incubation period in a disease model. , 2009 .

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

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

[19]  Ron A M Fouchier,et al.  Antigenic and Genetic Characteristics of Swine-Origin 2009 A(H1N1) Influenza Viruses Circulating in Humans , 2009, Science.

[20]  M. E. Alexander,et al.  Modelling strategies for controlling SARS outbreaks , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[21]  A. K. Misra,et al.  Effect of awareness programs by media on the epidemic outbreaks: A mathematical model , 2013, Appl. Math. Comput..

[22]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[23]  Bjoern Peters,et al.  Pre-existing immunity against swine-origin H1N1 influenza viruses in the general human population , 2009, Proceedings of the National Academy of Sciences.

[24]  I. Kiss,et al.  The impact of information transmission on epidemic outbreaks. , 2010, Mathematical biosciences.

[25]  Chengjun Sun,et al.  Global results for an SIRS model with vaccination and isolation , 2010 .

[26]  Zheng Xing,et al.  Preexisting Immunity to Pandemic (H1N1) 2009 , 2009, Emerging infectious diseases.

[27]  Xueyong Zhou,et al.  Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate , 2011 .

[28]  Mick G. Roberts,et al.  Quarantine-based disease control in domesticated animal herds , 1998 .

[29]  M. Li,et al.  Global dynamics of a SEIR model with varying total population size. , 1999, Mathematical Biosciences.

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

[31]  Joydip Dhar,et al.  The role of viral infection in phytoplankton dynamics with the inclusion of incubation class , 2010 .

[32]  Mohammad A. Safi,et al.  Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine , 2011, Comput. Math. Appl..

[33]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[34]  J. Hyman,et al.  Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model , 2008, Bulletin of mathematical biology.

[35]  Carlos Castillo-Chavez,et al.  On the Computation of R(o) and Its Role on Global Stability , 2001 .

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

[37]  Jinde Cao,et al.  Impact of media coverage on epidemic spreading in complex networks , 2013, Physica A: Statistical Mechanics and its Applications.

[38]  Anuj Mubayi,et al.  A cost-based comparison of quarantine strategies for new emerging diseases. , 2010, Mathematical biosciences and engineering : MBE.

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

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

[41]  Abba B. Gumel,et al.  Global asymptotic dynamics of a model for quarantine and isolation , 2010 .

[42]  P. Zhao,et al.  Pre-Existing Immunity with High Neutralizing Activity to 2009 Pandemic H1N1 Influenza Virus in Shanghai Population , 2013, PloS one.

[43]  Abba B. Gumel,et al.  Dynamics of a model with quarantine-adjusted incidence and quarantine of susceptible individuals , 2012, Journal of Mathematical Analysis and Applications.

[44]  Yun Zou,et al.  Optimal and sub-optimal quarantine and isolation control in SARS epidemics , 2007, Mathematical and Computer Modelling.

[45]  Huaiping Zhu,et al.  Media/psychological impact on multiple outbreaks of emerging infectious diseases , 2007 .

[46]  Nathan W. Stebbins,et al.  Glycan Receptor Binding of the Influenza A Virus H7N9 Hemagglutinin , 2013, Cell.

[47]  M. Rothstein.  QUARANTINE AND ISOLATION: LESSONS LEARNED FROM SARS , 2003 .

[48]  N. Britton,et al.  On the Dynamics of a Two-Strain Influenza Model with Isolation , 2012 .

[49]  M. Blaser,et al.  Critical role of nosocomial transmission in the toronto sars outbreak. , 2004, Mathematical biosciences and engineering : MBE.

[50]  Libo Dong,et al.  Cross-reactive antibody responses to the 2009 pandemic H1N1 influenza virus. , 2009, The New England journal of medicine.

[51]  Robert G. McLeod,et al.  Sensitivity and uncertainty analyses for a sars model with time-varying inputs and outputs. , 2006, Mathematical biosciences and engineering : MBE.

[52]  Shigui Ruan,et al.  Simulating the SARS outbreak in Beijing with limited data , 2003, Journal of Theoretical Biology.

[53]  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.

[54]  Jia Li,et al.  A mathematical model for control of vector borne diseasesthrough media campaigns , 2013 .

[55]  Carlos Castillo-Chavez,et al.  Dynamical models of tuberculosis and their applications. , 2004, Mathematical biosciences and engineering : MBE.

[56]  Maoxing Liu,et al.  Analysis of an epidemic model with awareness programs by media on complex networks , 2013 .

[57]  Anupama Sharma,et al.  EFFECT OF AWARENESS PROGRAMS IN CONTROLLING THE PREVALENCE OF AN EPIDEMIC WITH TIME DELAY , 2011 .

[58]  Joydip Dhar,et al.  Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate , 2012 .

[59]  Yanni Xiao,et al.  A Filippov system describing media effects on the spread of infectious diseases , 2013, Nonlinear Analysis: Hybrid Systems.

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

[61]  James E. Crowe,et al.  Structural Basis of Preexisting Immunity to the 2009 H1N1 Pandemic Influenza Virus , 2010, Science.

[62]  C. Wichems,et al.  Response to a monovalent 2009 influenza A (H1N1) vaccine. , 2009, The New England journal of medicine.

[63]  E O Powell,et al.  Theory of the chemostat. , 1965, Laboratory practice.