Extensive Analysis and Projection of the Impact of High-Risk Immunity Using a Mathematical Model That Incorporates a Convex Incidence Rate of Multiple Covid-19 Exposures

Yıl 2023, Cilt: 20 Sayı: 2, 106 - 128, 01.11.2023

Mutairu Kayode Kolawole , Morufu Oyedunsi Olayıwola Adedapo Ismaila Alaje Abidoye Kazeem Odeyemı

Öz

In this research study, we investigate the impact of multiple exposure of individuals on the prevalence of COVID-19 and the efficacy of high-risk immunity measures in controlling its transmission dynamics. Through a qualitative analysis of a mathematical model, which includes the positivity of solutions, existence and uniqueness of solutions, and study of invariant regions, we demonstrate that the model can be utilized to examine pandemic outbreaks in a physical system. Our analysis of the basic reproductive ratio reveals that the implementation of high-risk immunity can reduce the number of
secondary infections even in scenarios of multiple exposures. Numerical simulations, based on real-life COVID-19 data from the Nigeria center for disease control, were conducted using the homotopy perturbation method, yielding results that support the outcome of the basic reproductive ratio analysis and providing insight into strategies to mitigate the spread of the disease.

Anahtar Kelimeler

COVID-19, Incidence rate, High risk immunity, Homotopy perturbation method.

Kaynakça

• [1] R.C. Del, and P.N. Malani, “Covid-19 New insights on a rapidly changing epidemic,” JAMA, vol. 323, no. 14, pp. 1339-1340, 2020.
• [2] WHO (World Health Organization) “2020 Emergencies, preparedness, response. Pneumonia of unknown originChina, Disease Outbreak News,” https://www.who.int/csr/don/05-january-2020-pneumonia-of-unkowncausechina/en/ (accessed 5 March 2020).
• [3] C. C. Lai, T. P. Shih, W. C. Ko, H. J. Tang, and P. R. Hsueh, “Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and coronavirus disease-2019 (COVID-19): The epidemic and the challenges,” International journal of antimicrobial agents, vol. 55, no. 3, pp. 105924, 2020.
• [4] Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, R. Ren, K. S. Leung, E.H. Lau, J.Y. Wong, and X. Xing, “Early transmisson dynamics in Wuhan China of novel coronavirus infected pneumonia,” The New England journal of medicine, vol. 382, no. 13, pp. 1199-1207, 2020.
• [5] F. Bozkurt, A. Yousef, T. Abdeljawad, A. Kalini, Q. Al Mdallal, “A fractional order model of COVID-19 considering the fear effect of the media and social networks on the community,” Chaos, Solitons and Fractals, vol. 152, pp. 111403, 2021.
• [6] R. U. Din, E. A. Algehyne, “Mathematical analysis of COVID-19 by using SIR model with convex incidence rate,” Result in Physics, vol. 23, pp. 103970, 2021.
• [7] R. U. Din, K. Shah, I. Ahmad, T. Abdeljawad, “Study of transmission dynamics of novel COVID-19 by using mathematical model,” Advances in Difference Equations, vol. 2020, pp. 323, 2020.
• [8] O. J. Peter, S. Qureshi, A. Yusuf, M. Al-Shomrani, and A. A. Idowu, “A new mathematical model of COVID-19 using real data from Pakistan,” Results in Physics, vol. 24, pp. 104098, 2021.
• [9] L. Wang, F. Xinjie, S. Yongzheng, and L. Maoxing, “Dynamical Analysis of a mathematical model of COVID-19 Spreading on Networks,” Frontiers in Physics, vol. 8, 2021.
• [10] R. U. Din, and E. A. Algehyne, “Mathematical analysis of COVID-19 by using SIR model with convex incidence rate,” Result in Physics, vol. 23, pp. 103970, 2021.
• [11] A. Khan, R. Zarin, G. Hussain, N.A. Ahmad, M. H. Mohd, and A. Yusuf, “Stability analysis and optimal control of Covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan),” Results Physics, vol. 20, pp. 103703, 2021.
• [12] O. J. Peter, S. Qureshi, S. Yusuf, M. Shomrani, and A. A. Idowu, “A new mathematical model of COVID-19 using real data from Pakistan,” Results in Physics, vol. 24, pp. 104098, 2021.
• [13] A. I. Alaje, M. O. Olayiwola, M. O. Ogunniran, J. A. Adedeji, and K. A. Adedokun, “Approximate analytical methods for the solution of fractional order integro-differential equations,” Nigerian Journal of Mathematics and Applications, vol. 31, pp. 175-190, 2021.
• [14] S. Triambak, D. P. Mahapatra, N. Mallick, and R. Sahoo, “A new logistic growth model applied to COVID-19 fatality data,” Epidemics, vol. 37, pp. 100515, 2021.
• [15] A. Babaei, H. Jafari, S. Banihashemi, and M. Ahmadi, “Mathematical analysis of a stochastic model for spread of Coronavirus,” Chaos Solitions Fractals, vol. 145, pp. 110788.
• [16] A.O. Yunus, M. O. Olayiwola, K. A. Adedokun, J. A. Adedeji, and A. I. Alaje, “Mathematical analysis of fractionalorder Caputo’s derivative of coronavirus disease model via Laplace Adomian decomposition method,” Beni-Suef Univ J Basic Appl Sci, vol. 11, no. 144, 2022.
• [17] C. Xu, Z. Liu, Y. Pang, and A. Akgül, “Stochastic analysis of a COVID-19 model with effects of vaccination and different transition rates: Real data approach,” Chaos, Solitons and Fractals, vol. 170, pp. 113395, 2023.
• [18] J. H. He,”Homotopy perturbation technique, ” Comput. Methods. Appl. Mech. Eng. vol. 178, pp. 257-262. 1999.
• [19] S. Balamuralitharan, and S. Geethamalini, “Solutions of epidemic of EIAV infection by HPM,” Journal of Physics. Conf.Series, vol. 1000, pp. 012023, 2018.
• [20] M. K. Kolawole, A. I. Alaje, M. O. Ogunniran, and K. R. Tijani, “Simulating the effect of disease transmission coefficient on a disease induced death seirs epidemic model using the homotopy perturbation method,” Journal of Applied Computer Science & Mathematics, vol. 16, no. 33, 2022.
• [21] M. O. Olayiwola, A. W. Gbolagade, and F. O. Akinpelu, “An efficient algorithm for solving the nonlinear PDE,” International Journal of Scientific and Engineering Research, vol. 2, no. 10, pp. 1-10, 2011.
• [22] M. O. Ogunniran, Y. Haruna, and R. B. Adeniyi, and M. O. Olayiwola, “Optimized three-step hybrid block method for stiff problems in ordinary differential equation,” Çankaya University Journal of Humanities and Social Sciences, vol. 17, pp. 80-95, 2020.
• [23] M. O. Olayiwola, F. O. Akinpelu, and A. W. Gbolagade, “Modified variational iteration method for the solution of a class of differential equations,” American Journal of Computational and Applied Mathematics, vol. 2, no. 5, pp.228-231, 2012.
• [24] Ikeja City Population [Online] Accessed (26-12-2022). https://citypopulation.de/en/nigeria/admin/lagos/NGA025011__ikeja.
• [25] M. Caputo, “Elasticita e Dissipazione,” Zanichelli, Bologna 14, 1969.
• [26] M. Caputo, and M. Fabrizio, “A new defnition of fractional derivative without singular kernel,” Prog. Fract. Difer. Appl. vol. 1, no. 2, pp. 73–85, 2016.
• [27] A. Atangana, and D. Baleanu, “New fractional derivatives with non-local and nonsingular kernel theory and application to heat transfer model,” Therm. Sci. vol. 20, pp. 763–769, 2016.