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DOI：http://dx.doi.org/10.26855/abr.2022.12.001

# Optimal Control Analysis of COVID-19 Transmission Model with Physical Distance and Treatment

Date: December 8,2022 |Hits: 1878 Download PDF How to cite this paper

Faizunnesa Khondaker1,2, Md. Kamrujjaman2,*, Md. Shahidul Islam2

1Department of Mathematics, Jagannath University, Dhaka, Bangladesh.

2Department of Mathematics, University of Dhaka, Dhaka, Bangladesh.

*Corresponding author: Md. Kamrujjaman

### Abstract

The transmission dynamics with optimal control of the novel COVID-19 pandemic is formulated and analyzed through a deterministic model using different human compartments. This research work investigated the effect of different control strategies in the form of physical distance and treatment. The basic reproduction number, R* is calculated and used to perform sensitivity analysis to identify the most influential parameters in disease transmission. Optimal control theory and Pontryagin’s maximum principle are used to optimize the model and obtain important optimality conditions to reduce disease burden. Optimal control analysis and numerical simulations reveal that the combined implementation of physical distance and treatment as interventions is more effective than other single control strategies discussed in this study and which yields a good result in reducing infection.

### References

[1] World Health Organization, “Coronavirus Disease 2019 (COVID-19), Situation Report -51, Data as reported by 11 March 2020”. https://www.who.int/emergencies/disease/ novel-coronavirus-2019/situation-reports.

[2] Tang, B., Bragazzi, N. L., Li, Q., Tang, S., Xiao, Y., and Wu, J. (2020). An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infectious Disease Modelling, 5, 248–255. https://doi.org/10.1016/j.idm.2020.02.001.

[3] He, S., Tang, S. Y., and Rong, L. (2020). A discrete stochastic model of the COVID-19 outbreak: Forecast and control. Mathematical biosciences and engineering: MBE, 17(4), 2792–2804. https://doi.org/10.3934/mbe.2020153.

[4] World Health Organization. “Coronavirus Disease 2019 (COVID-19), Situation Report -25”. https://www.who.int/ emergen-cies/disease/novel-coronavirus-2019/situation-reports.

[5] Lu H. (2020). Drug treatment options for the 2019-new coronavirus (2019-nCoV). Bioscience trends, 14(1), 69–71.

https://doi.org/10.5582/bst.2020.01020.

[6] Madubueze, C.E., Kimbir, A.R. and Aboiyar, T. (2018). Global Stability of Ebola Virus Disease Model with Contact Tracing and Qu-arantine..Applications & Applied Mathematics, 13(1), 382–403.

[7] Hassan, M. N., Mahmud, M. S., Nipa, K. F., and Kamrujjaman, M. (2021). Mathematical Modeling and COVID-19 Forecast in Texas, USA: A Prediction Model Analysis and the Probability of Disease Outbreak. Disaster medicine and public health preparedness, 1–12. Advance online publication. https://doi.org/10.1017/dmp.2021.151.

[8] Omame, A., Rwezaura, H., Diagne, M. L., Inyama, S. C., and Tchuenche, J. M. (2021). COVID-19 and dengue co-infection in Brazil: optimal control and cost-effectiveness analysis. European physical journal plus, 136(10), 1090.

https://doi.org/10.1140/epjp/s13360-021-02030-6.

[9] Abidemi, A., Zainuddin, Z. M., and Aziz, N. A. B. (2021). Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study. European physical journal plus, 136(2), 237.https://doi.org/10.1140/epjp/s13360-021-01205-5.

[10] Madubueze, C. E., Dachollom, S., and Onwubuya, I. O. (2020). Controlling the Spread of COVID-19: Optimal Control Analysis. Computational and mathematical methods in medicine, 2020, 6862516. https://doi.org/10.1155/2020/6862516.

[11] Zamir, M., Abdeljawad T., Nadeem F., Wahid A. and Yousef, A. (2021). An optimal control analysis of a COVID-19 model. Alexandria Engineering Journal, 60(3), 2875-2884. doi:10.1016/j.aej.2021.01.022.

[12] Song, H., Wang, R., Liu, S., Jin, Z., and He, D. (2022). Global stability and optimal control for a COVID-19 model with vaccination and isolation delays. Results in physics, 42, 106011. https://doi.org/10.1016/j.rinp.2022.106011.

[13] Kamrujjaman, M., Mahmud, M. S., and Islam, M. S. (2020). Coronavirus Outbreak and the Mathematical Growth Map of COVID-19. Annual Research & Review in Biology, 35(1), 72-78. https://doi.org/10.9734/arrb/2020/v35i130182.

[14] Olaniyi, S., Obabiyi, O. S., Okosun, K. O., Oladipo, A. T., and Adewale, S. O. (2020). Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics. European physical journal plus, 135(11), 938.

https://doi.org/10.1140/epjp/s13360-020-00954-z.

[15] Khan, M. A., Ullah, S., and Kumar, S. (2021). A robust study on 2019-nCOV outbreaks through non-singular derivative. European physical journal plus, 136(2), 168. https://doi.org/10.1140/epjp/s13360-021-01159-8.

[16] Aba Oud, M. A., Ali, A., Alrabaiah, H., Ullah, S., Khan, M. A., and Islam, S. (2021). A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load. Advances in difference equations, 2021(1), 106. https://doi.org/10.1186/s13662-021-03265-4.

[17] Tsay, C., Lejarza, F., Stadtherr, M. A., and Baldea, M. (2020). Modeling, state estimation, and optimal control for the US COVID-19 outbreak. Scientific reports, 10(1), 10711. https://doi.org/10.1038/s41598-020-67459-8.

[18] Abidemi, A., Zainuddin, Z. M., and Aziz, N. A. B. (2021). Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study. European physical journal plus, 136(2), 237. https://doi.org/10.1140/epjp/s13360-021-01205-5.

[19] Ullah, S., and Khan, M. A. (2020). Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study. Chaos, solitons, and fractals, 139, 110075. https://doi.org/10.1016/j.chaos.2020.110075.

[20] Mwalili, S., Kimathi, M., Ojiambo, V., Gathungu, D., and Mbogo, R. (2020). SEIR model for COVID-19 dynamics incorporating the environment and social distancing. BMC research notes, 13(1), 352. https://doi.org/10.1186/s13104-020-05192-1.

[21] Kamrujjaman, M., Saha, P., Islam, M.S. and Ghosh, U. (2022). Dynamics of SEIR Model: A case study of COVID-19 in Italy. Results in Control and Optimization, 7, 100119. https://doi.org/10.1016/j.rico.2022.100119.

[22] Mahmud, M. S., Kamrujjaman, M., Adan, M. M. Y., Hossain, M. A., Rahman, M. M., Islam, M. S., Mohebujjaman, M., and Molla, M. M. (2022). Vaccine efficacy and SARS-CoV-2 control in California and U.S. during the session 2020-2026: A modeling study. Infec-tious Disease Modelling, 7(1), 62–81. https://doi.org/10.1016/j.idm.2021.11.002.

[23] Avila-Ponce de León, U., Pérez, Á. G. C., and Avila-Vales, E. (2020). An SEIARD epidemic model for COVID-19 in Mexico: Ma-thematical analysis and state-level forecast. Chaos, solitons, and fractals, 140, 110165. https://doi.org/10.1016/j.chaos.2020.110165.

[24] Chitnis, N., Hyman, J. M., and Cushing, J. M. (2008). Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bulletin of mathematical biology, 70(5), 1272–1296. https://doi.org/10.1007/s11538-008-9299-0.

[25] Pontryagin, L.S., Boltyanskii, V.G., Gamkrelize, R.V. and Mishchenko, E.F. (1962). The Mathematical Theory of Optimal Processes. John Wiley & Sons, New York.

[26] Fleming, W.H. and Rishel, R.W. (1975). Deterministic and Stochastic Optimal Control. Springer, Berlin.

[27] Lakshmikantham, V., Leela, S., and Martynyuk, A.A. (1989). Stability Analysis of Nonlinear Systems. Marcel Dekker Inc., New York.

[28] Imran, M., Malik, T., Ansari, A. R., and Khan, A. (2016). Mathematical analysis of swine influenza epidemic model with optimal control. Japan journal of industrial and applied mathematics, 33(1), 269–296. https://doi.org/10.1007/s13160-016-0210-3.

[29] Hethcote, H.W. (2000). The mathematics of infectious diseases. SIAM Rev., 42(4), 599–653.

https://doi.org/10.1137/S0036144500371907.

[30] Islam, MS, Ira, JI, Kabir, KMA, Kamrujjaman, M. (2020). Effect of lockdown and isolation to suppress the COVID-19 in Bangladesh: an epidemic compartments model, Journal of Applied Mathematics and Computation, 4 (3), 83-93.

[31] Kamrujjaman, M., Mahmud, MS et al. (2021). SARS-CoV-2 and Rohingya refugee camp, Bangladesh: uncertainty and how the government took over the situation. Biology, 10 (2), 124.

### How to cite this paper

Optimal Control Analysis of COVID-19 Transmission Model with Physical Distance and Treatment

How to cite this paper: Faizunnesa Khondaker, Md. Kamrujjaman, Md. Shahidul Islam. (2022) Optimal Control Analysis of COVID-19 Transmission Model with Physical Distance and Treatment. Advance in Biological Research3(1), 65-76.

DOI: http://dx.doi.org/10.26855/abr.2022.12.001