zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Effect of media-induced social distancing on disease transmission in a two patch setting. (English) Zbl 1211.92051
Summary: We formulate an SIS epidemic model on two patches. In each patch, media coverage about the cases present in the local population leads individuals to limit the number of contacts they have with others, inducing a reduction in the rate of transmission of the infection. A global qualitative analysis is carried out, showing that the typical threshold behavior holds, with solutions either tending to an equilibrium without disease, or the system being persistent and solutions converging to an endemic equilibrium. Numerical analysis is employed to gain insight in both the analytically tractable and intractable cases; these simulations indicate that media coverage can reduce the burden of the epidemic and shorten the duration of the disease outbreak.

MSC:
92D30Epidemiology
34C60Qualitative investigation and simulation of models (ODE)
37N25Dynamical systems in biology
65C20Models (numerical methods)
WorldCat.org
Full Text: DOI
References:
[1] Arguin, P. M.; Navin, A. W.; Steele, S. F.; Weld, L. H.; Kozarsky, P. E.: Health communication during SARS, Emerg. infectious dis. 10, No. 2, 377 (2004)
[2] Arino, J.: Diseases in metapopulations, Series in contemporary applied mathematics 11, 65-123 (2009)
[3] Arino, J.; Jordan, R.; Den Driessche, P. Van: Quarantine in a multi-species epidemic model with spatial dynamics, Math. biosci. 206, No. 1, 46 (2007) · Zbl 1124.92042 · doi:10.1016/j.mbs.2005.09.002
[4] Baroyan, V. O.; Rvachev, L. A.: Deterministic epidemic models for a territory with a transport network, Kibernetica 3, 67 (1967)
[5] Bergeron, S. L.; Sanchez, A. L.: Media effects on students during SARS outbreak, Emerg. infectious dis. 11, No. 5, 732 (2005)
[6] Blendon, R. J.; Benson, J. M.; Desroches, C. M.; Raleigh, E.; Taylor-Clark, K.: The public’s response to severe acute respiratory syndrome in Toronto and the united states, Clin. infectious dis. 38, No. 7, 925 (2004)
[7] Blendon, R. J.; Koonin, L. M.; Benson, J. M.; Cetron, M. S.; Pollard, W. E.; Mitchell, E. W.; Weldon, K. J.; Herrmann, M. J.: Public response to community mitigation measures for pandemic influenza, Emerg. infectious dis. 14, No. 5, 778 (2008)
[8] Brownstein, J. S.; Freifeld, C. C.; Madoff, L. C.: Influenza A (H1N1) virus, 2009 -- online monitoring, New england J. Med. 360, No. 21, 2156 (2009)
[9] Castillo-Chavez, C.; Thieme, H.: Asymptotically autonomous epidemic models, Mathematical population dynamics: analysis of heterogeneity, 33 (1995)
[10] Cui, J.; Sun, Y.; Zhu, H.: The impact of media on the control of infectious diseases, J. dyn. Differ. eqn. 20, No. 8, 31 (2008) · Zbl 1160.34045 · doi:10.1007/s10884-007-9075-0
[11] Cui, J.; Tao, X.; Zhu, H.: An SIS infection model incorporating media coverage, Rocky mt. J. math. 38, No. 5, 1323 (2008) · Zbl 1170.92024 · doi:10.1216/RMJ-2008-38-5-1323
[12] Diekmann, O.; Heesterbeek, J. A. P.; Metz, J. A.: On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. math. Biol. 28, No. 4, 365 (1990) · Zbl 0726.92018 · doi:10.1007/BF00178324
[13] Ekunwe, E. O.; Taylor, P.; Macauley, R.; Ayodele, O.: How disease prevention fails without good communication, World health forum 15, No. 4, 340 (1994)
[14] Jones, J. H.; Salathé, M.: Early assessment of anxiety and behavioral response to novel swine-origin influenza $A(H1N1)$, Plos one 4, No. 12, e8032 (2009)
[15] K. Khan, J. Arino, R. Eckhardt, M. Gardam, W. Hu, D. Kossowsky, M. MacDonald, J. Sears, J. Wang, Global air traffic patterns during the H1N1 influenza pandemic and their public health implications -- a report of the Bio.Diaspora Project to the Public Health Agency of Canada. Technical report, St. Michael’s Hospital, 2011.
[16] Khan, K.; Arino, J.; Hu, W.; Raposo, P.; Sears, J.; Calderon, F.; Heidebrecht, C.; Macdonald, M.; Liauw, J.; Chan, A.; Gardam, M.: Spread of a novel influenza A (H1N1) virus via global airline transportation, New england J. Med. 361, No. 2, 212 (2009)
[17] Khan, M. A.; Rahman, M.; Khanam, P. A.; Khuda, B.; Kane, T. T.; Ashraf, A.: Awareness of sexually transmitted disease among women and service providers in rural bangladesh, Int. J. STD AIDS 8, No. 11, 688 (1997)
[18] Liu, R.; Wu, J.; Zhu, H.: Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. math. Methods med. 8, No. 3, 153 (2007) · Zbl 1121.92060 · doi:10.1080/17486700701425870
[19] Mykhalovskiy, E.; Weir, L.: The global public health intelligence network and early warning outbreak detection: a canadian contribution to global public health, Can. J. Public health 97, No. 1, 42 (2006)
[20] Perko, L.: Differential equations and dynamical systems, (1996) · Zbl 0854.34001
[21] Perlman, G. Y.: The influence of an event in the israeli media on the compliance of patients with influenza vaccinations in the winter of 2006 -- 2007, Harefuah 148, No. 12, 811-814 (2009)
[22] Porter, R. W.; Steinglass, R.; Kaiser, J.; Olkhovsky, P.; Rasmuson, M.; Dzhatdoeva, F. A.; Fishman, B.; Bragina, V.: Role of health communications in Russia’s diphtheria immunization program, J. infect dis. 181, No. Suppl 1, S220 (2000)
[23] Global Influenza Programme. Pandemic influenza preparedness and response -- a WHO guidance document. Technical report, World Health Organization, 2009.
[24] Rahman, M. S.; Rahman, M. L.: Media and education play a tremendous role in mounting AIDS awareness among married couples in bangladesh, AIDS res. Ther. 4, 10 (2007)
[25] Smith, H. L.; Waltman, P.: The theory of the chemostat, (1995) · Zbl 0860.92031
[26] Den Driessche, P. Van; Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. biosci. 180, 29 (2002) · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6
[27] Wallis, P.; Nerlich, B.: Disease metaphors in new epidemics: the UK media framing of the 2003 SARS epidemic, Social sci. Med. 60, No. 11, 2629-2639 (2005)
[28] Wilson, N.; Thomson, G.; Mansoor, O.: Print media response to SARS in New Zealand, Emerg. infectious dis. 10, No. 8, 1461 (2004)
[29] Xiao, D.; Ruan, S.: Global analysis of an epidemic model with nonmonotone incidence rate, Math. biosci. 208, 419 (2007) · Zbl 1119.92042 · doi:10.1016/j.mbs.2006.09.025
[30] Zhao, X.: Dynamical systems in population biology, (2003) · Zbl 1023.37047