Modeling the transmission dynamics of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) with latent immigrants

References

• A. N. Alagaili, T. Briese, N. Mishra, V. Kapoor, S. C. Sameroff, E. de Wit, V. J. Munster, L. E. Hensley, I. S. Zalmout, A. Kapoor, J. H. Epstein, W. B. Karesh, P. Daszak, O. B. Mohammed, W. I. Lipkin. Middle East Respiratory Syndrome Coronavirus Infection in Dromedary Camels in Saudi Arabia, mBio 5 (2) (2014), e00884–14, doi:10.1128/mBio.00884–14.
   PubMed Web of Science ®Google Scholar
• A. Assiri, A. McGeer, T. M. Perl, C. S. Price, A. A. Al Rabeeah, D. A. T. Cummings, Z. N. Alabdullatif, M. Assad, A. Almulhim, H. Makhdoom, H. Madani, R. Alhakeem, J. A. Al-Tawfiq, M. Cotten, S. J. Watson, P. Kellam, A. I. Zumla, and Z. A. Memish, Hospital outbreak of Middle East Respiratory Syndrome Coronavirus, N Engl J Med 369 (5) (2013) 407–416. doi: 10.1056/NEJMoa1306742
   PubMed Web of Science ®Google Scholar
• A. Bermingham, M. A. Chand, C. S. Brown, E. Aarons, C. Tong, C. Langrish, K. Hoschler, K. Brown, M. Galiano, R. Myers, R. G. Pebody, H. K. Green, N. L. Boddington, R. Gopal, N. Price, W. Newsholme, C. Drosten, R. A. Fouchier and M. Zambon, Severe respiratory illness caused by a novel coronavirus, in a patient transferred to the United Kingdom from the Middle East. Euro Surveill,17 (40) (2012).
   Google Scholar
• F. Brauer, P. van den Driessche, Models for the transmission of disease with immigration of infectives, Math. Biosci. 171, 2001 143–154. doi: 10.1016/S0025-5564(01)00057-8
   PubMed Web of Science ®Google Scholar
• C. Castillo-Chavez, Z. Feng and W. Huang (2002), On the computation of R0 and its role on global stability. In: C. Castillo-Chavez, S. Blower, P. van der Driessche, D. Kirschner, and A. Yakubu (eds) Mathematical approaches for emerging and reemerging infectious diseases:an introduction, Springer (2002) 261–274.
   Google Scholar
• C. Castillo-Chavez, B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Engineer. 1(2) (2004) 361–404 doi: 10.3934/mbe.2004.1.361
   PubMed Web of Science ®Google Scholar
• S. Cauchemez, C. Fraser, M. D. V. Kerkhove, C. A. Donnelly, S. Riley, A. Rambaut, V. Enouf, S. van der Werf, N. M. Ferguson, Middle East respiratory syndrome coronavirus: quantification of the extent of the epidemic, surveillance biases, and transmissibility, Lancet Infect Dis, 14 (2014) 50–56. doi: 10.1016/S1473-3099(13)70304-9
   PubMed Web of Science ®Google Scholar
• CIDRAP Center for infectious diseases research and policy, University of Minnesota (2014) http://www.cidrap.umn.edu/news-perspective/2013/09/eight-472new-saudi-cases-push-global-mers-total-130 (Accessed September 14 2014).
   Google Scholar
• R. J. de Groot, S. C. Baker, R. S. Baric, C. S. Brown, C. Drosten, L. Enjuanes, R. A. M. Fouchier, M. Galiano, A. E. Gorbalenya, Z. A. Memish, S. Perlman, L. L. M. Poon, E. J. Snijder, G. M. Stephens, P. C. Y. Woo, A. M. Zaki, M. Zambon and J. Ziebuhr, Middle East Respiratory Syndrome Coronavirus (MERS-CoV): Announcement of the Coronavirus Study Group. J. Virol., 87(14) (2013) 7790–7792. doi: 10.1128/JVI.01244-13
   PubMed Web of Science ®Google Scholar
• Gloval overview of an emerging novel coronavirus (MERS-CoV), World Health Assembly (2013).
   Google Scholar
• A. B. Gumel, S. Ruan, T. Day, J. Watmough, F. Brauer, P. van den Driessche, D. Gabrielson, C. Bowman, M. E. Alexander, S. Ardal, J. Wu and B. M. Sahai, Modelling strategies for controlling SARS outbreaks, Proc. R. Soc. Lond. B 271 (2004) 2223–2232. doi: 10.1098/rspb.2004.2800
   PubMed Web of Science ®Google Scholar
• H. Guo, M. Y. Li, Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations, Discrete Contin. Dyn. Syst., Ser. B, 17(7) (2012) 2413–2430. doi: 10.3934/dcdsb.2012.17.2413
   Web of Science ®Google Scholar
• B. L. Haagmans, S. H. S. Al Dhahiry, C. B. E. M. Reusken, V. S. Raj, M. Galiano, R. Myers, G.-J. Godeke, M. Jonges, E. Farag, A. Diab, H. Ghobashy, F. Alhajri, M. Al-Thani, S. A. Al-Marri, H. E. Al Romaihi, A. Al Khal, A. Bermingham, A. D. M. E. Osterhaus, M. M. AlHajri and M. P. G. Koopmans, Middle East respiratory syndrome coronavirus in dromedary camels: an outbreak investigation, Lancet Infect Dis, 14 (2014) 140–45. doi: 10.1016/S1473-3099(13)70690-X
   PubMed Web of Science ®Google Scholar
• J.K. Hale, S.M.V. Lunel, Introduction to functional differential equations, Springer-Verlag, Berlin, Heidelrberg, New York, 1993.
   Google Scholar
• HealthMap organization (2014). http://www.healthmap.org/en/ (Accessed March 14 2014).
   Google Scholar
• M. G. Hemidal, R. A. Perera, P. Wang, M. A. Alhammadi, L. Y. Siu, M. Li, L. L. Poon, L. Saif, A. Alnaeem and M. Peiris, Middle East Respiratory Syndrome (MERS) coronavirus seroprevalence in domestic livestock in Saudi Arabia, 2010 to 2013, Euro Surveill, 18 (50) (2013) pii=20659. Available online: http://www.eurosurveillance.org/.
   Google Scholar
• K. Kupperschmidt, Researchers scramble to understand camel connection to MERS, SCIENCE, 341 (2013).
   Web of Science ®Google Scholar
• J. Lee, G. Chowell, and E. Jung, A dynamic compartmental model for the middle east respiratory syndrome outbreak in the republic of korea: A retrospective analysis on control interventions and superspreading events, Journal of theoretical biology, 408 (2016) 118–126. doi: 10.1016/j.jtbi.2016.08.009
   PubMed Web of Science ®Google Scholar
• P. Lancaster, Theory of Matrices, New York, (1969).
   Google Scholar
• P. M. Penttinen, K. Kaasik-Aaslav, A. Friaux, A. Donachie, B. Sudre, A. J. Amato-Gauci, Z. A. Memish, D. Coulombier, Taking stock of the first 133 MERS coronavirus cases globally – Is the epidemic changing? Euro Surveill, 18 (39) (2013) 1–5. doi: 10.2807/1560-7917.ES2013.18.39.20596
   PubMedGoogle Scholar
• R. A. Perera, P. Wang, M. R. Gomaa, R. El-Shesheny, A. Kandeil, O. Bagato, L. Y. Siu, M. M. Shehata, A. S. Kayed, Y. Moatasim, M. Li, L. L. Poon, Y. Guan, R. J. Webby, M. A. Ali, J. S. Peiris and G. Kayali (2013). Seroepidemiology for MERS coronavirus using microneutralisation and pseudoparticle virus neutralisation assays reveal a high prevalence of antibody in dromedary camels in Egypt, June 2013. Euro Surveill, 18 (36): pii=20574. Available online: http://www.eurosurveillance.org/ViewArticle.aspx?ArticleId=20574. doi: 10.2807/1560-7917.ES2013.18.36.20574
   Google Scholar
• C. B. Reusken, M. Ababneh, V. S. Raj, B. Meyer, A. Eljarah, S. Abutarbush, G. J. Godeke, T. M. Bestebroer, I. Zutt, M. A. Müller, B. J. Bosch, P. J. Rottier, A. D. Osterhaus, C. Drosten, B. L. Haagmans and M. P. Koopmans, Middle East Respiratory Syndrome coronavirus (MERS-CoV) serology in major livestock species in an affected region in Jordan, June to September 2013, Euro Surveill, 18 (50) (2013) pii=20662. Available online: //www.eurosurveillance.org/View-Article.aspx?ArticleId=20662. doi: 10.2807/1560-7917.ES2013.18.50.20662
   Google Scholar
• M.A Safi, A.B. Gumel, Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine, Computers and Mathematics with applications, 61 (2011) 3044–3070. doi: 10.1016/j.camwa.2011.03.095
   Web of Science ®Google Scholar
• M.A Safi, A.B. Gumel, Qualitative study of a quarantine/isolation model with multiple disease stages, Applied Mathematics and Computation 218 (2011) 1941–1961. doi: 10.1016/j.amc.2011.07.007
   Web of Science ®Google Scholar
• World Health Organization (WHO) (2014). Global Alert and Response (GAR): Middle East respiratory syndrome coronavirus (MERS-CoV) – update //www.who.int/csr/don/20140411mers/en/ (accessedApril21,2014) (accessed April 21, 2014).
   Google Scholar
• World Health Organization (WHO). Global Alert and Response (GAR): novel coronavirus infection http://www.who.int/csr/don/20130801/en/index.html (accessed Aug 1, 2014).
   Google Scholar
• Z.-Q. Xia, J. Zhang, Y.-K. Xue, G.-Q. Sun, and Z. Jin, Modeling the transmission of middle east respiratory syndrome corona virus in the republic of korea, PloS one, 10 (2015), p. e0144778. doi: 10.1371/journal.pone.0144778
   PubMed Web of Science ®Google Scholar
• A. M. Zaki, S. van Boheemen, T. M. Bestebroer, A. D.M.E. Osterhaus, and R. A.M. Fouchier, Isolation of a Novel Coronavirus from a Man with Pneumonia in Saudi Arabia. N Engl J Med, 367 (2012) 1814–1820. doi: 10.1056/NEJMoa1211721
   PubMed Web of Science ®Google Scholar