Analysis of SIR epidemic model with information spreading of awareness

Abstract The information spreading of awareness can prompt the manners of human to ease the infectious possibility and assist to recover swiftly. A dynamic system of Susceptible-Infected-Recovered (SIR) with Unaware-Aware (UA) process (SIR-UA) is newly developed by using compartment model through analytical approach with assumption of an infinite and well-mixed population. Moreover, individuals in a population can be classified into six states as unaware susceptible(SU), aware susceptible(SA), unaware infected(IU), aware infected(IA), unaware recovered(RU), and aware recovered(RA). Compared with previous models, the new dynamic set of equations described the more widespread situation and incorporated all possible states of Unaware-Aware (UA) with SIR process. The effect of awareness is explored carefully to show the significance on epidemic model with time steps. Consequently, the properties of parameters on the epidemic awareness model are studied to deliberate different physical situations. Finally, full phase diagrams are explored to show the epidemic sizes of susceptible and recovered individuals for various parameters.

[1]  M. Faiz,et al.  Chikungunya Outbreak in Dhaka: Lessons for Bangladesh , 2017 .

[2]  Chongjun Fan,et al.  Effect of individual behavior on the interplay between awareness and disease spreading in multiplex networks , 2016 .

[3]  Zhen Jin,et al.  Pattern transitions in spatial epidemics: Mechanisms and emergent properties , 2016, Physics of Life Reviews.

[4]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[5]  Steve Gregory,et al.  Efficient local behavioral change strategies to reduce the spread of epidemics in networks , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Niraj Pandit,et al.  Awareness and practice about preventive method against mosquito bite in Gujarat. , 2010 .

[7]  Romualdo Pastor-Satorras,et al.  Effect of risk perception on epidemic spreading in temporal networks , 2017, Physical review. E.

[8]  Sergio Gómez,et al.  Competing spreading processes on multiplex networks: awareness and epidemics , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  WILLIAM GOFFMAN,et al.  Generalization of Epidemic Theory: An Application to the Transmission of Ideas , 1964, Nature.

[10]  Thilo Gross,et al.  Epidemic dynamics on an adaptive network. , 2005, Physical review letters.

[11]  Americo Cunha,et al.  Calibration of a SEIR-SEI epidemic model to describe the Zika virus outbreak in Brazil , 2018, Appl. Math. Comput..

[12]  Christel Kamp,et al.  Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics , 2009, PLoS Comput. Biol..

[13]  Lin Wang,et al.  Coupled disease–behavior dynamics on complex networks: A review , 2015, Physics of Life Reviews.

[14]  M. Salathé,et al.  The effect of opinion clustering on disease outbreaks , 2008, Journal of The Royal Society Interface.

[15]  Jun Tanimoto,et al.  Which is more effective for suppressing an infectious disease: imperfect vaccination or defense against contagion? , 2018 .

[16]  Yaohui Pan,et al.  The impact of multiple information on coupled awareness-epidemic dynamics in multiplex networks , 2018 .

[17]  Peter Stechlinski,et al.  Application of control strategies to a seasonal model of chikungunya disease , 2015 .

[18]  Guanrong Chen,et al.  Epidemic control and awareness , 2014 .

[19]  Jie Zhang,et al.  Community Size Effects on Epidemic Spreading in Multiplex Social Networks , 2016, PloS one.

[20]  Alessandro Vespignani,et al.  Invasion threshold in heterogeneous metapopulation networks. , 2007, Physical review letters.

[21]  Michael Small,et al.  The impact of awareness on epidemic spreading in networks , 2012, Chaos.

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

[23]  V. Joseph Hotz,et al.  The Responsiveness of the Demand for Condoms to the Local Prevalence of AIDS , 1996 .

[24]  Ming Tang,et al.  Suppressing disease spreading by using information diffusion on multiplex networks , 2016, Scientific Reports.

[25]  Alessandro Vespignani,et al.  Modeling human mobility responses to the large-scale spreading of infectious diseases , 2011, Scientific reports.

[26]  Jun Tanimoto,et al.  Fundamentals of Evolutionary Game Theory and its Applications , 2015 .

[27]  Xin Jiang,et al.  Two-stage effects of awareness cascade on epidemic spreading in multiplex networks. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Sergio Gómez,et al.  On the dynamical interplay between awareness and epidemic spreading in multiplex networks , 2013, Physical review letters.

[29]  Liang’an Huo,et al.  Dynamical interplay between the dissemination of scientific knowledge and rumor spreading in emergency , 2016 .

[30]  Zhen Jin,et al.  Transmission dynamics of cholera: Mathematical modeling and control strategies , 2017, Commun. Nonlinear Sci. Numer. Simul..

[31]  Reuven Cohen,et al.  Complex Networks: Structure, Robustness and Function , 2010 .

[32]  Dawei Zhao,et al.  Competing spreading processes and immunization in multiplex networks , 2016, ArXiv.

[33]  Pietro Liò,et al.  The Impact of Heterogeneity and Awareness in Modeling Epidemic Spreading on Multiplex Networks , 2016, Scientific Reports.

[34]  Harry Eugene Stanley,et al.  Epidemics on Interconnected Networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Zhen Jin,et al.  Hemorrhagic fever with renal syndrome in China: Mechanisms on two distinct annual peaks and control measures , 2018 .

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