Geodesic
Optimal control strategy to control pandemic Covid-19 using MSILIHR_V Model
Shahriar Seddighi Chaharborj1 ; Jalal Hassanzadeh Asl1 ; Babak Mohammadi2
1 Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2 Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran
Mathematical modelling of natural phenomena, Tome 17 (2022), article no. 23.

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Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed a MSIlIhR-V mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobian matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model’s stability and instability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of COVID-19 from 4 January, 2021 up to 14 June, 2021 in Iran. Maple and MATLAB software’s will be used for programming. We will use Maple software for analytical parts and MATLAB software for numerical and simulation parts.
DOI : 10.1051/mmnp/2022015

Shahriar Seddighi Chaharborj 1 ; Jalal Hassanzadeh Asl 1 ; Babak Mohammadi 2

1 Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2 Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran 
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Shahriar Seddighi Chaharborj; Jalal Hassanzadeh Asl; Babak Mohammadi. Optimal control strategy to control pandemic Covid-19 using MSILIHR_V Model. Mathematical modelling of natural phenomena, Tome 17 (2022), article  no. 23. doi : 10.1051/mmnp/2022015. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2022015/

[1] D. Adak, A. Majumder, N. Bairagi Mathematical perspective of Covid-19 pandemic: Disease extinction criteria in deterministic and stochastic models Chaos Solitons Fractals 2021 110381

[2] S.Y. Araz Analysis of a Covid-19 model: optimal control, stability and simulations Alexandria Eng. J. 2021 647 658

[3] B.A. Baba, B. Bilgehan Optimal control of a fractional order model for the COVID-19 pandemic Chaos Solitons Fract. 2021 110678

[4] A. Baleta, Dramatic drop in SA’s immunization rates. Spotlight, 24 June 2020.

[5] S.P. Blythe, C. Castillo-Chavez, J.S. Palmer, M. Cheng Toward a unified theory of sexual mixing and pair formation Math. Biosci. 1991 379 405

[6] S. Busenberg and C. Castillo-Chavez, Interaction pair formation and force of infection terms in sexually transmitted disease, in vol. 83 Mathematical and Statistical Approaches to AIDS Epidemiology, edited by Castillo-Chavez. Lecture Notes in Biomathematics. Springer-Verlag, New York (1989) 289–300.

[7] K. Causey, N. Fullman, R.J. Sorensen, N.C. Galles, P. Zheng, A. Aravkin and J.F. Mosser, Estimating global and regional disruptions to routine childhood vaccine coverage during the COVID-19 pandemic in 2020: a modelling study. The Lancet (2021).

[8] S. Chandir, D.A. Siddiqi, H. Setayesh, A.J. Khan Impact of COVID-19 lockdown on routine immunisation in Karachi, Pakistan Lancet Global Health 2020 e1118 e1120

[9] S.S. Chaharborj, M. Rizam Abu Bakar and N. Akma Ibrahim, Deterministic and Stochastic Models for HIV. LAP Lambert Academic Publishing, Germany (2013).

[10] S.S. Chaharborj, M.R.A. Bakar, A. Ebadian Disease transmission MSEIR model with individuals traveling between patches i and i + 1 J. Appl. Math. Inf. 2010 1073 1088

[11] S.S. Chaharborj, M. Rizam Abu Bakar and N. Akma Ibrahim, Deterministic and Stochastic Models for HIV. LAP Lambert Academic Publishing, Germany (2013).

[12] S.L. Chang, N. Harding, C. Zachreson, O.M. Cliff, M. Prokopenko Modelling transmission and control of the COVID-19 pandemic in Australia Nat. Commun. 2020 1 13

[13] S.S. Chaharborj, I. Fudziah, M.A. Bakar, R.S. Chaharborj, Z.A. Majid, A.G.B. Ahmad The use of generation stochastic models to study an epidemic disease Adv. Differ. Equ. 2013 1 9

[14] S.S. Chaharborj, M.R.A. Bakar, A. Ebadian Disease transmission MSEIR model with individuals traveling between patches i and i + 1 J. Appl. Math. Inf. 2010 1073 1088

[15] R. Chowdhury, K. Heng, M.S.R. Shawon, G. Goh, D. Okonofua, C. Ochoa-Rosales, O.H. Franco Dynamic interventions to control COVID-19 pandemic: a multivariate prediction modelling study comparing 16 worldwide countries Eur. J. Epidemiol. 2020 389 399

[16] C.T. Deressa, G.F. Duressa Modeling and optimal control analysis of transmission dynamics of COVID-19: The case of Ethiopia Alexandria Eng. J. 2021 719 732

[17] A. D’Onofrio, P. Manfredi Bifurcation thresholds in an SIR model with information-dependent vaccination Math. Model. Natur. Phenom. 2007 26 43

[18] O. Diekmann, J.A.P. Heesterbeek, J.A. Metz On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations J. Math. Biol. 1990 365 382

[19] O. Diekmann, J.A.P. Heesterbeek, J.A. Metz On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations J. Math. Biol. 1990 365 382

[20] L. Di Domenico, G. Pullano, C.E. Sabbatini, P.Y. Boëlle, V. Colizza Modelling safe protocols for reopening schools during the COVID-19 pandemic in France Nat. Commun. 2021 1 10

[21] L. Di Domenico, G. Pullano, C.E. Sabbatini, P.-Y. Boëlle, V. Colizza Impact of lockdown on COVID-19 epidemic in Île-de-France and possible exit strategies BMC Med. 2020 240

[22] P. Eichmeir, T. Lauß, S. Oberpeilsteiner, K. Nachbagauer, W. Steiner The adjoint method for time-optimal control problems J. Comput. Nonlinear Dyn. 2021

[23] H. Ferjouchia, A. Kouidere, O. Zakary, M. Rachik Optimal control strategy of COVID-19 spread in morocco using SEIRD model Moroccan J. Pure Appl. Anal. 2021 66 79

[24] S. Flaxman Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe Nature 2020 257 261

[25] N. Haug Ranking the effectiveness of worldwide COVID-19 government interventions Nat. Hum. Behav. 2020 1303 1312

[26] H.W. Hethcote The mathematics of infectious diseases SIAM Rev. 2000 599 653

[27] S. Hsiang The effect of large-scale anti-contagion policies on the COVID-19 pandemic Nature 2020 262 267

[28] N. Keshri, B.K. Mishra Optimal control model for attack of worms in wireless sensor network Int. J. Grid Distrib. Comput. 2014 251 272

[29] Z.S. Lassi, R. Naseem, R.A. Salam, F. Siddiqui, J.K. Das The impact of the COVID-19 pandemic on immunization campaigns and programs: a systematic review Int. J. Environ. Res. Public Health 2021 988

[30] P. Martens How will climate change affect human health? Am. Sci. 1999 534 541

[31] B.G. Masresha, R. Luce Jr, M.E. Shibeshi, B. Ntsama, N’A. Diaye, J. Chakauya, R. Mihigo The performance of routine immunization in selected African countries during the first six months of the COVID-19 pandemic Pan Afri. Med. J. 2020

[32] K. Mulholland, K. Kretsinger, L. Wondwossen, N. Crowcroft Action needed now to prevent further increases in measles and measles deaths in the coming years The Lancet 2020 1782 1784

[33] P.A. Naik, J. Zu, K.M. Owolabi Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control Chaos Solitons Fract. 2020 109826

[34] National Health Commission (NHC) of the People’s Republic of China (2020). NHC daily reports. http://www.nhc.gov.cn/ yjb/pzhgli/new_list.shtml.

[35] F. Pegoraro, S.V. Bulanov Nonlinear, nondispersive wave equations: Lagrangian and Hamiltonian functions in the hodograph transformation Phys. Lett. A 2020 126064

[36] A. Raza, A. Ahmadian, M. Rafiq, S. Salahshour, M. Ferrara An analysis of a nonlinear susceptible-exposed- infected-quarantine-recovered pandemic model of a novel coronavirus with delay effect Results Phys. 2020 103771

[37] A. Raza, A. Ahmadian, M. Rafiq, S. Salahshour, M. Ferrara An analysis of a nonlinear susceptible-exposed- infected-quarantine-recovered pandemic model of a novel coronavirus with delay effect Results Phys. 2020 103771

[38] M.A. Shereen, S. Khan, A. Kazmi, N. Bashir and R. Siddique, COVID-19 infection: origin, transmission, and characteristics of human coronaviruses. J. Adv. Res. (2020).

[39] C.J. Silva, C. Cruz, D.F. Torres, A.P. Munuzuri, A. Carballosa, I. Area, J. Mira Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal Sci. Rep. 2021 1 15

[40] C. Tsay, F. Lejarza, M.A. Stadtherr, M. Baldea Modeling, state estimation, and optimal control for the US COVID-19 outbreak Sci. Rep. 2020 1 12

[41] P. Van Den Driessche, J. Watmough Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission Math. Biosci. 2002 29 48

[42] P.G. Walker, C. Whittaker, O. Watson et al., The global impact of COVID-19 and strategies for mitigation and suppression. London: WHO Collaborating Centre for Infectious Disease Modelling, MRC Centre for Global Infectious Disease Analysis, Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London (2020).

[43] C. Wang, P.W. Horby, F.G. Hayden, G.F. Gao A novel coronavirus outbreak of global health concern Lancet 2020 470 473

[44] WHO, Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19) (WHO, 2020).

[45] WHO, Pulse survey on continuity of essential health services during the COVID-19 pandemic (2020).

[46] WHO, Statement following the twenty-eighth IHR emergency committee for polio. https://www.who.int/news/item/21-05-2021-statement-following-the-twenty-eighth-ihr-emergency-committee-for-polio.

[47] World Health Organization, Coronavirus disease (COVID-2019) situation reports (2020). https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports. Accessed 15 April 2020.

[48] World Health Organization. Global immunization news (GIN) June 2020. Immunization and COVID-19. Second pulse Poll to help understand disruptions to vaccination and how to respond.

[49] The Worldometer (2020). COVID-19 CORONAVIRUS PANDEMIC. https://www.worldometers.info/coronavirus/. Accessed 15 April 2020.

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