Effects of acceptance of enlightenment on COVID-19 transmission using homotopy perturbation method

Tawakalt Abosede Ayoola, Mutairu Kayode Kolawole, Amos Oladele Popoola

Abstract


The deadly Corona virus disease has had a significantly devastating impact on the general public, necessitating the study of transmission dynamics. A mathematical model of a non-linear differential equation for COVID-19 infection is investigated with the effects of some basic factors, such as the acceptance of enlightenment to avoid being exposed and the acceptance of enlightenment to go for vaccination. The basic reproduction number, which determines the disease’s spread, is calculated. The local and global stability analyses of the model are carried out. The sensitivity analysis is also computed. Numerical simulation using the homotopy perturbation method demonstrates the effect of the acceptance of enlightenment on the population. Our results indicate that when the populace accepts vaccination, the rate at which COVID-19 spreads reduces.


Keywords


COVID-19; Global Stability; Enlightenment; Homotopy Perturbation Method

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References


K. Roosa, Y. Lee, R. Luo, A. Kirpich, R. Rothenberg, J. Hyman, P. Yan, and G. Chowell, “Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020,” Infectious Disease Modelling, vol. 5, pp. 256–263, 2020. DOI: 10.1016/j.idm.2020.02.002

O. A. Adegboye, A. I. Adekunle, and E. Gayawan, “Early transmission dynamics of novel Coronavirus (COVID-19) in Nigeria,” International Journal of Environmental Research and Public Health, vol. 17, no. 9, p. 3054, 2020. DOI: 10.3390/ijerph17093054

M. V. Krishna and J. Prakash, “Mathematical modelling on phase based transmissibility of Coronavirus,” Infectious Disease Modelling, vol. 5, pp. 375–385, 2020. DOI: 10.1016/j.idm.2020.06.005

N. Ferguson et al., “Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand,” Imperial College London, 2020. DOI: 10.25561/77482

T. A. Ayoola, M. K. Kolawole, and A. O. Popoola, “Mathematical Model of COVID-19 Transmission Dynamics with Double Dose Vaccination,” Tanzania Journal of Science, vol. 48, no. 2, pp. 499–512, 2022. DOI: 10.4314/tjs.v48i2.23

X. Wang, “Studying social awareness of physical distancing in mitigating COVID-19 transmission,” Mathematical Biosciences and Engineering, vol. 17, no. 6, pp. 7428–7441, 2020. DOI: 10.3934/mbe.2020380

M. A. Balya et al., “Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model,” Communication in Biomathematical Sciences, vol. 4, no. 1, pp. 46–64, 2021. DOI: 10.5614/cbms.2021.4.1.5

S. S. Musa, S. Qureshi, S. Zhao, A. Yusuf, U. T. Mustapha, and D. He, “Mathematical modeling of COVID-19 epidemic with effect of awareness programs,” Infectious Disease Modelling, vol. 6, pp. 448–460, 2021. DOI: 10.1016/j.idm.2021.01.012

G. Adomian, “A review of the decomposition method and some recent results for nonlinear equations,” Computers & Mathematics with Applications, vol. 21, no. 5, pp. 101–127, 1991. DOI: 10.1016/0898-1221(91)90220-X

J.-H. He, “Variational iteration method – a kind of non-linear analytical technique: some examples,” International Journal of Non Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. DOI: 10.1016/S0020-7462(98)00048-1

J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257-262, 1999. DOI: 10.1016/S0045-7825(99)00018-3

S. Balamuralitharan and S. Geethamalini, “Solutions of the epidemic of EIAV infection by HPM,” Journal of Physics: Conference Series, vol. 1000, no. 1, p. 012023, 2018. DOI: 10.1088/1742-6596/1000/1/012023

A. Alaje, M. Olayiwola, M. Ogunniran, J. Adedeji, and K. Adedokun, “Approximate Analytical methods for the solution of Fractional Order Integrodifferential equation,” Nigerian Journal of Mathematics and Applications, vol. 31, p. 175, 2021.

O. Chandrow, “Forcasting COVID-19 pandemic in Bangladesh by using Homotopy perturbation Method,” Journal of Mathematics (IOSR-JM), 2021.

M. M. Jumanne and S. Z. Naboth, “Mathematical Model of COVID-19 transmission Dynamics and Control Strategies,” journal of Applied and Computation Math, vol. 9, 2020.

B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Tang, Y. Xiao, and J. Wu, “Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions,” Journal of Clinical Medicine, vol. 9, no. 2, p. 462, 2020. DOI: 10.3390/jcm9020462

A. Babaei, H. Jafari, S. Banihashemi, and M. Ahmadi, “Mathematical analysis of a stochastic model for spread of Coronavirus,” Chaos, Solitons & Fractals, vol. 145, p. 110788, 2021. DOI: 10.1016/j.chaos.2021.110788

C. T. Deressa, Y. O. Mussa, and G. F. Duressa, “Optimal control and sensitivity analysis for transmission dynamics of Coronavirus,” Results in Physics, vol. 19, p. 103642, 2020. DOI: 10.1016/j.rinp.2020.103642

S. M. Garba, J. M.-S. Lubuma, and B. Tsanou, “Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa,” Mathematical Biosciences, vol. 328, p. 108441, 2020. DOI: 10.1016/j.mbs.2020.108441

M. Yavuz, F. Ö. Coşar, F. Günay, and F. N. Özdemir, “A New Mathematical Modeling of the COVID-19 Pandemic Including the Vaccination Campaign,” Open Journal of Modelling and Simulation, vol. 09, no. 03, pp. 299–321, 2021. DOI: 10.4236/ojmsi.2021.93020

J. Zhang, J. Dean, Y. Yin, D. Wang, Y. Sun, Z. Zhao, and W. J, “Determinants of covid-19 vaccine acceptance and hesitancy: a health care student - based online survey in northwest china.” Frontiers in Public Health, vol. 9, 2022. DOI: 10.3389/fpubh.2021.777565

O. Diekmann and J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, ser. Wiley Series in Mathematical & Computational Biology. Wiley, 2000. ISBN 9780471492412.

C. Castillo-Chavez and B. Song, “Dynamical Models of Tuberculosis and Their Applications,” Mathematical Biosciences and Engineering, vol. 1, no. 2, pp. 361–404, 2004. DOI: 10.3934/mbe.2004.1.361




DOI: https://doi.org/10.34312/jjbm.v3i2.15798

Copyright (c) 2022 Tawakalt Abosede Ayoola, Mutairu Kayode Kolawole, Amos Oladele Popoola

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