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Analyzing the MERS disease control strategy through an optimal control problem

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A deterministic mathematical model of the Middle East respiratory syndrome (MERS) disease is introduced. Medical masks, supportive care treatment and a government campaign about the importance of medical masks will be involved in the model as time dependent variables. The problem is formulated as an optimal control one to minimize the number of infected people and keep the intervention costs as low as possible. Assuming that all control variables are constant, we find a disease free equilibrium point and an endemic equilibrium point explicitly. The existence and local stability criteria of these equilibria depend on the basic reproduction number. A sensitivity analysis of the basic reproduction number with respect to control parameters tells us that the intervention on medical mask use and the campaign about the importance of medical masks are much more effective for reducing the basic reproduction number than supportive care intervention. Numerical experiments for optimal control problems are presented for three different scenarios, i.e., a scenario of different initial conditions for the human population, a scenario of different initial basic reproduction numbers and a scenario of different budget limitations. Under budget limitations, it is much better to implement the medical mask intervention in the field, rather than give supportive care to control the spread of the MERS disease in the endemic prevention scenario. On the other hand, the medical mask intervention should be implemented partially together with supportive care to obtain the lowest number of infected people, with the lowest cost in the endemic reduction scenario.
Rocznik
Strony
169--184
Opis fizyczny
Bibliogr. 30 poz., rys., tab., wykr.
Twórcy
autor
  • Department of Mathematics, University of Indonesia (UI), Kampus UI Depok, Depok 16424, Indonesia
autor
  • Department of Mathematics, University of Indonesia (UI), Kampus UI Depok, Depok 16424, Indonesia
autor
  • Department of Mathematics, University of Indonesia (UI), Kampus UI Depok, Depok 16424, Indonesia
  • Department of Mathematics, University of Indonesia (UI), Kampus UI Depok, Depok 16424, Indonesia
autor
  • Department of Mathematics, University of Indonesia (UI), Kampus UI Depok, Depok 16424, Indonesia
Bibliografia
  • [1] Abboubakar, M., Kamgang, J. and Tieudjo, D. (2015). Backward bifurcation and control in transmission dynamics of arboviral diseases, Mathematical Biosciences 278(1): 100–129.
  • [2] Al-Tawfiq, J., Smallwood, C., Arbuthnott, K., Malik, M.S., Barbeschi, M. and Memish, Z. (2012). Emerging respiratory and novel coronavirus 2012 infections and mass gatherings, East Mediterr Health Journal 19(1): 48–54.
  • [3] Aldila, D., Nuraini, N. and Soewono, E. (2014). Optimal control problem of preventing of swine flu disease transmission, Applied Mathematical Science 8(71): 3501–3512.
  • [4] Aldila, D., Soewono, E. and Nuraini, N. (2012). On the analysis of effectiveness in mass application of mosquito repellent for dengue disease prevention, AIP Conference Proceedings 1450(1): 103–109.
  • [5] Assiri, A., McGeer, A., Perl, T., Price, C., Al Rabeaah, A. and Cummings, D. (2013). Hospital outbreak of Middle East respiratory syndrome coronavirus, The New England Journal of Medicine 369(5): 407–416.
  • [6] Cauchemez, S., Fraser, C., Van Kerkhove, M., Donnelly, C., Riley, S. and Rambaut, A. (2014). Middle East respiratory syndrome coronavirus: Quantification of the extent of the epidemic, surveillance biases, and transmissibility, Lancet Infectious Diseases 14(1): 5056.
  • [7] Chowell, G., Blumberg, S., Simonsen, L., Miller, M. and Viboud, C. (2014). Synthesizing data and models for the spread of MERS-CoV, 2013: Key role of index cases and hospital transmission, Epidemics 9(1): 40–51.
  • [8] Diekmann, O. and Heesterbeek, J. (2000). Mathematical Epidemiology of Infectious Diseases, Model Building, Analysis and Interpretation, John Wiley & Son, Chichester.
  • [9] Diekmann, O., Heesterbeek, J. and Metz, J. (1990). On the definition and the computation of the basic reproduction ratio of R0 in models of infectious disease in heterogeneous populations, Journal of Mathematical Biology 28(4): 365–382.
  • [10] Diekmann, O., Heesterbeek, J. and Roberts, M. (2010). The construction of next-generation matrices for compartmental epidemic models, Journal of The Royal Society Interface 7(47): 873–885.
  • [11] Ejima, K., Aihara, K. and Nishiura, H. (2014). Probabilistic differential diagnosis of Middle East respiratory syndrome (MERS) using the time from immigration to illness onset among imported cases, Journal of Theoretical Biology 346(1).
  • [12] Gautret, P. (2013). Middle East respiratory syndrome (MERS) coronavirus: What travel health advice should be given to Hajj pilgrims?, Travel Medicine and Infectious Disease 11(5): 263–265.
  • [13] Gerberry, D. (2016). Practical aspects of backward bifurcation in a mathematical model for tuberculosis, Journal of Theoretical Biology 388(1): 15–36.
  • [14] Haagmans, B., Al Dhahiry, S., Reusken, C., Raj, V. and Galiano, M. (2014). Middle East respiratory syndrome coronavirus in dromedary camels: An outbreak investigation, Lancet Infectious Diseases 14(2): 140–145.
  • [15] Malik, T.M., Alsaleh, A.A., Gumel, A.B. and Safi, M.A. (2015). Optimal strategies for controlling the MERS coronavirus during a mass gathering, Global Journal of Pure and Applied Mathematics 11(6): 4831–4865.
  • [16] Muller, M., Meyer, B., Corman, V., Al-Masri,M., Turkestani, A. and Ritz, D. (2015). Presence of Middle East respiratory syndrome coronavirus antibodies in Saudi Arabia: A nationwide, cross-sectional, serological study, Lancet Infectious Diseases 15(5): 559–564.
  • [17] Novkaniza, F., Ivana and Aldila, D. (2016). Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model, AIP Conference Proceedings 1723(1): 030015–10, DOI: 10.1063/1.4945073.
  • [18] Obaid, H.A., Ouifki, R. and Patidar, K.C. (2013). An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection, International Journal of Applied Mathematics and Computer Science 23(2): 357–372, DOI: 10.2478/amcs-2013-0027.
  • [19] Okuonghae, D. (2013). A mathematical model of tuberculosis transmission with heterogeneity in disease susceptibility and progression under a treatment regime for infectious cases, Applied Mathematical Modelling 37(10–11): 6786–6808.
  • [20] Omrani, A., Abdul-Mutin, M., Haddad, Q., Al-Nakhli, D., Memish, Z. and Albarrak, A. (2013). A family cluster of Middle East respiratory syndrome coronavirus infectious related to a likely unrecognized asymptomatic or mild case, International Journal of Infectious Disease 17(9): 668–672.
  • [21] Paez Chavez, J., Gotz, T., Siegmund, S. and Wijaya, K. (2017). An SIR-Dengue transmission model with seasonal effects and impulsive control, Mathematical Biosciences 289(2): 29–39.
  • [22] Pattnaik, S., Bakwad, K., Sohi, B., Ratho, R. and Devi, S. (2013). Swine influenza models based optimization (SIMBO), Applied Soft Computing 13(1): 628–653.
  • [23] Poletto, C., Pelat, C., Levy-Bruhl, D., Yazdanpanah, Y., Boelle, P.-Y. and Colizza, V. (2014). Assessment of the Middle East respiratory syndrome coronavirus (MERS-COV) epidemic in the Middle East and risk of international spread using a novel maximum likelihood analysis approach, Eurosurveillance 19(23): 20824.
  • [24] Reusken, C.B.E.M., Haagmans, B.L., Muller, M.A., Gutierrez, C., Godeke, G.J., Meyer, B.,Muth, D., Raj, V.S., Smits-De Vries, L., Corman, V.M., Drexler, J.-F., Smits, S.L., El Tahir, Y.E., De Sousa, R., van Beek, J., Nowotny, N., van Maanen, K., Hidalgo-Hermoso, E., Bosch, B.J., Rottier, P., Osterhaus, A., Gortazar-Schmidt, C., Drosten, C. and Koopmans, M.P.G. (2013). Middle East respiratory syndrome coronavirus neutralising serum antibodies in dromedary camels: A comparative serological study, Lancet Infectious Diseases 13(10): 859–866.
  • [25] Saha, S. and Roy, P.K. (2017). A comparative study between two systems with and without awareness in controlling HIV/AIDS, International Journal of Applied Mathematics and Computer Science 27(2): 337–350, DOI: 10.1515/amcs-2017-0024.
  • [26] WHO (2013). Revised interim case definition for reporting to WHO—Middle East respiratory syndrome coronavirus (MERS-CoV), www.who.int/csr/disease/coronavirus_infections/case_definition_03_07_2014/en/.
  • [27] WHO (2016). Middle East respiratory syndrome coronavirus (MERS-CoV), www.who.int/mediacentre/factsheets/mers-cov/en.
  • [28] Xia, Z.-Q., Zhang, J., Xue, Y.-K., Sun, G.-Q. and Jin, Z. (2015). Modeling the transmission of Middle East respirator syndrome corona virus in the Republic of Korea, PLoS ONE 10(12): e0144778.
  • [29] Xu, Z. and Ai, C. (2016). Traveling waves in a diffusive influenza epidemic model with vaccination, Applied Mathematical Modelling 40(15–16): 7265–7280.
  • [30] Zaki, A., van Boheemen, S., Bestebroer, T., Osterhaus, A. and Fouchier, R. (2012). Isolation of a novel coronavirus from a man with pneumonia in Saudi Arabia, The New England Journal of Medicine 367(19): 1814–1820.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-eb62f6fb-e3de-4dd7-ae83-4ddb07300e0e
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