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Impact of Optimal Control Techniques on Dual-Bilinear Treatment Protocols for COVID-19 Pandemic

Bassey Echeng Bassey

Department of Mathematics, Cross River University of Technology, Calabar, Nigeria.

*Corresponding author: Bassey Echeng Bassey

Date: August 9,2022 Hits: 432


In enacting the goal for possible eradication of the budding COVID-19 pandemic and acknowledging the presence of epileptic availability and uncertain potent of vaccines, the present study adopted and extended the model by Bassey and Atsu (2021) to investigate the impact of optimal control protocols for the treatment dynamics of COVID-19 infection. Initiated by the transformation of the basic model to an optimal control problem, optimal characterization of the model was investigated followed by the establishment of the existence of optimal controls for COVID-19 pandemic. The study explored classical Pontryagin’s maximum principle with the incorporation of Hessian matrix for the investigation and analysis of model optimality system and its uniqueness of solutions. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, we further presented numerical validations of established theoretical predictions. Results of numerical simulations indicated that with the application of optimal control technique under dual-bilinear optimal control functions, maximal reduction of COVID-19 transmission was highly achieved within 3-18 days with insignificant resurgence of the viral load thereafter. The study therefore, affirmed that under sustained cogent adherence to designated dual-bilinear optimal controls, optimal control technique is an efficient tool for the methodological control of COVID-19 and its related infectious diseases.


[1] Torres, DFM, Ndaïrou, F, Area, I, Nieto, JJ. Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan. Chaos, Solitons and Fractals, http://ees.elsevier.com; 2020 [accessed 02, September, 2020]. 

[2] Gumel, AB. (2020). Using mathematics to understand and control the coronavirus pandemic, https://opinion.premiumtimesng. com/2020/05/04/using-mathematics tounderstand-and-control-the-coronavirus-pandemic-by-abba-b-gumel/; 2020 [accessed 16, August, 2020].

[3] Nita, HS, Ankush, HS, Ekta, NJ. (2020). Control strategies to curtail transmission of COCID-19. Intl. J. Maths. and Mathcal. Sc., 2020; 1-12. http://downloads.hindawi.com/journals/ijmms/2020/2649514.pdf. 

[4] World Health Organization. (2020). COVID-19 Weekly Epidemiological Update, https://www.who.int/publications/m/item/ weekly-epidemiological-update---27-october-2020; 2020 [accessed 27, October, 2020].

[5] Nigeria Centre for Disease Control. (2020). Coronavirus disease (COVID-19) pandemic, https://ncdc.gov.ng/#; 2020 [accessed 27, October, 2020].

[6] Grigorieva, E, Khailov, E, Korobeinikov, A. (2020). Optimal quarantine strategies for COVID-19 control models. https://arxiv.org/pdf/ 2004.10614.pdf; 2020 [accessed 29, August, 2020].

[7] Leslie, M. (2020). T cells found in coronavirus patients 'bode well' for long-term immunity, http://science.sciencemag.org/ content/368/6493/809; 2020 [accessed 14, August, 2020].

[8] Bassey, E. B., Atsu, U. J. (2021). Global stability analysis of the role of multi-therapies and non-pharmaceutical treatment protocols for COVID-19 pandemic. Chaos, Solitons and Fractals, 143(2021), 110574. https://pubmed.ncbi.nlm.nih.gov/33519116/.

[9] Jahanshahi, H., Yousefpour, A., Bekires, S. (2020). Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak. Chaos, Solitons and Fractals, 2020; 136: 1-6. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7229919/. 

[10] Wu, JT, Leung, K, Leung, GM. (2020). Nowcasting and forecasting the potential domestic and international spread of the 2019.nCoV outbreak originating in Wuhan, China: a modeling study. The Lacet 2020; 395(10225):689-697. https://www.thelancet.com/action/showPdf?pii=S0140-6736%2820%2930260-9.

[11] Peng, L, Yang, W, Zhang, D, Zhuge, C, Hong, L. (2020). Epidemic analysis of COVID-19 in China by dynamical modeling, http://arxiv.org/abs/2002.06563; 2020 [accessed 14, August, 2020]. 

[12] Obsu, LL, Balcha, FS. (2020). Optimal control strategies for the transmission risk of COVID-19. Journal of Biological Dynamics 2020; 14(1): 590-607. https://www.tandfonline.com/doi/full/10.1080/17513758.2020.1788182.

[13] Moore, SE, Okyere, E. (2020). Controlling the transmission dynamics of COVID-19. ArXiv. 2020; 2004.00443, https://arxiv.org/pdf/2004.00443.pdf; 2020 [accessed 10 August, 2020].

[14] Sasmita, NR, Ikhwan, M, Suyanto, S, Chongsuvivatwong, V. (2020). Optimal control on a mathematical model to pattern the progression of coronavirus disease 2019 (COVID-19) in Indonesia. Global Health Research and Policy 2020; 5(38): 1-12. https://ghrp.biomedcentral.com/articles/10.1186/s41256-020-00163-2.    

[15] Lee, D, Nasud, MA, Kim, BN, Oh, C. (2017). Optimal control analysis for the MEERS-CoV outbreak: South Korea perspectives. J. Korea Soc. Indust. Appl. Math 2017; 21(3): 143-154. http://koreascience.or.kr/article/JAKO201728441290805.pdf. 

[16] Imai, N, Cori, A, Dorigatti, I, et al. (2020). MRC Centre for Global Infectious Disease Analysis: Wuhan coronavirus reports 1-3, https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-transmissibility-25-01-2020.pdf; 2020 [accessed 21 November, 2020].

[17] Wahid, BKA, Moustapha, D, Rabi, HG, Bisso, S. (2020). Contribution to the Mathematical Modeling of COVID-19 in Niger. Applied Mathematics 2020; 11: 427-435. https://doi.org/10.4236/am.2020.116030.

[18] AL-Husseiny, HF, Mohsen, AA, Zhou, X. (2020). A dynamical behavior of COVID-19 virus model with carrier effect to Out-break Epidemic. Research Square//Preprint, https://www.researchsquare.com/article/rs-24219/v1; 2020 [accessed 12, August, 2020].

[19] Danane, J, Allali, K. (2018). Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids. High-Throughput 2018; 7(35): 1-16. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6306857/. 

[20] Fister, KR, Lenhart, S, McNally, JS. (1998). Optimizing chemotherapy in an HIV Model. Electr. J. Diff. Eq. 1998; 32: 1-12. http://emis.matem.unam.mx/journals/EJDE/1998/32/fister.pdf 

[21] Hattaf, K, Yousfi, N. (2012). Optimal control of a delayed HIV infection model with immune response using an efficient numerical method. Biomathematics 2012; 1-7.

[22] Joshi, HR. (2002). Optimal Control of an HIV Immunology Model. Optimal Control Applications and Methods 2002; 23:199-213. http://www.math.utk.edu/~lenhart/docs/hiv.pdf. 

[23] Kahuru, J, Luboobi, L, Nkansah-Gyekye, Y. (2017). Optimal control techniques on a mathematical model for the dynamics of tungiasis in a community. Intl. J. Maths and Mathcal. Sc. 2017; 1-9. https://www.hindawi.com/journals/ijmms/2017/4804897/.

[24] Bassey, EB. (2021). Optimal multi-therapeutic protocols for the control of cholera mortality rate. 39th Annual Conference of the Nigeria Mathematical Society (NMS-RUN 2020), C40:(46). Retrieved date: [12, April, 2021], online available at https://www.app.nigerianmathematicalsociety.org/conference.  

[25] Fleming, W, Rishel, R. (1975). Deterministic and Stochastic Optimal Control. Springer Verlag: New York; 1975. http://dx.doi.org/10.1007/978-1-4612- 6380-7. 

[26] Culshaw, R, Ruan, S, Spiteri, RJ. (2004). Optimal HIV Treatment by Maximizing Immune Response. Journal of Mathematical Biology 2004; 48(5): 545-562. https://miami.pure.elsevier.com/en/publications/optimal-hiv-treatment-by-maximising-immun e-response.

[27] Bassey, BE. (2020). Optimal control dynamics: Multi-therapies with dual immune response for treatment of dual delayed HIV-HBV Infections. I.J. Mathematical Sciences and Computing 2020c; 6(2):18-60. http://www.mecs-press.org/ijmsc/ijmsc -v6-n2/IJMSC-V6-N2-2.pdf 

[28] Pontryagin, LS, Boltyanskii, VG, Gamkrelize, RV, Mishchenko, EF. (1967). The Mathematical Theory of Optimal Processes. Wiley: New York; 1967. https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.19630431023.

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Impact of Optimal Control Techniques on Dual-Bilinear Treatment Protocols for COVID-19 Pandemic

How to cite this paper:  Bassey Echeng Bassey. (2022) Impact of Optimal Control Techniques on Dual-Bilinear Treatment Protocols for COVID-19 Pandemic. Journal of Applied Mathematics and Computation6(3), 310-331.

DOI: http://dx.doi.org/10.26855/jamc.2022.09.004