Home Journals Books For Authors and Reviewers Online Submission News About Us Contact Us
Search
magazinelogo

Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 Downloads: 176491 Total View: 1991260
Frequency: quarterly ISSN Print: 2576-0645 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Search articles within this journal Submit an article

Journal Menu

Volumes & Issues

Current Issue

Download PDF

How to cite this paper

2295

TOTAL VIEWS

More Articles

Article Open Access http://dx.doi.org/10.26855/jamc.2023.06.008

Four-compartmental Epidemic and Endemic Dynamics Model for Delay Time γΙ(t)-Distributed Existing Average

Rasaki Olawale Olanrewaju1,*, Sodiq Adejare Olanrewaju2, Oluwafemi Samson Balogun3, Wasiu Adesoji Adepoju4

1Business Analytics and Value Networks (BAVNs), Mohammed VI Polytechnic University (UM6P), Rabat, Morocco.

2Department of Statistics, University of Ibadan, Ibadan, Nigeria.

3School of Computing, University of Eastern, F1-70211, Kuopio Campus, Finland.

4Department of Mathematics Education, University of Ibadan, Ibadan, Nigeria.

*Corresponding author: Rasaki Olawale Olanrewaju

Published: July 31,2023

Abstract

Four-Compartmental epidemic and endemic stability model for a population of persons to ascertain the transition of transmissible disease with their states of health was expounded. A person is said to fall in the category of either infected, susceptible, or recovery to give a four-compartmental model that transits S = sus-ceptible; C = categorized into the incubation stage; I = infected (ill); R= recovered, that consider a random interval of immunity that delays transition of  R→S. The structural Ordinary Differential Equation (ODE) of the SCIRS  model was derived, and the existence of the endemic stability was determined to ascertain how healthy the state is. The state will be categorized as unstable whenever γΙ(t)   possessed a fat-tail distribution coupled with an infinite mean. The proposed SCIR  transitional model was governed by the phenomenology of epidemic dynamics, such as the endemic stability and equilibrium, and asymptotic behavior for delay time with existing mean. The proposed model for the epidemic dynamics was subjected to Covid-19 reported cases in Nigeria for the period of March 2019 to December 2022 and it was deduced that the infectious rate is  B(t)=B[S(t), i(t), t]=10%≥0.

References

[1] Rihan, F.A.S. (2021). Delay Differential Equations, and Applications to Biology. Springer Nature, Singapore. 

[2] Kermack, W.O. and McKendrick, A.G. (1991). Contribution to the Mathematical Theory of Epidemics—III: Further Studies of the Problem of Endemicity. Bulletin of Mathematical Biology, 53(2), 89-118. doi.10.1007/BF02464425.

[3] Barsnarkov, L. Tomovski, I.Sandev, T. and Kocarev, L. (2021). Non-Markovian SIR Epidemic Spreading Model. ar-Xiv:2107.07427. 

[4] Kermack, W.O. and McKendrick, A.G. (1927). A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London A, 115, 700-721. 

[5] Olanrewaju, R.O. (2018). Bayesian Approach: An Alternative to Periodogram and TimeAxes Estimation for known and unknown White Noise. International Journal of Mathematical Sciences and Computing, 2(5), 22-33. doi.10.5815/ijmsc.2018.02.03.

[6] Julie, C. B. and Lauren, M.C. (2018). An Introduction to Compartmental Modeling for the Budding Infectious Disease Modeler. Letters in Biomathematics, 5(1), 195-221. doi.org/10.1080/2373786.2018.1509026. 

[7] Olanrewaju, R.O. Nafiu, L.A. Muse, A.H., and Barry, T.S. (2021). Stochastic Modelling of the Dynamics of the SARS-CoV-2 Epidemic: An Africa Perspective. American Journal of Mathematics and Statistics, 11(2), 41-48.

doi.10.5923/j.ajms.20211102.03.

[8] Liu, Y. Gayle, A.A. Wilder-Smith, A. and Rocklöv, J. (2020). The Reproductive Number of COVID-19 is Higher Compared to SARS Coronavirus, Journal of Travel Medicine, 27(2), doi.org/10.1093/jtm/taaa021.

[9] Bestehom, M. Michelitsch, T.M. Collet, B.A. Riascos, A.P. and Nowakowski, A. F. (2022). Simple Model of Epidemic Dynamics with Memory Effects. Phys. Rev. E 105, 024205.

[10] Olanrewaju, R.O. Barry, T.S. Muse, A.H. and Habineza, A. (2021). Ornstein-Uhlenbeck Processvia Conflated Drive of Brownian Motion and Lévy Process and its Application. Mathematical Theory and Modeling, 11(3), 12-20. www.iiste.orgISSN 2224-5804.

[11] Pereira, E.S. Galantini, J.A. and Duval, M.E. (2017). Use of a Three-Compartment Model to Evaluate the Dynamics of Cover Crop Residues. Archives of Agronomy and Soil Science, 1-7. http://dx.doi.org/10.1080/03650340.2017.1296137.

[12] Campbell, E.E. and Paustian, K. (2015). Current Developments in Soil Organic Matter Modeling and the Expansion of Model Applications: A Review. Environmental Research Letter, 10. 

[13] Nakamura, G. Grammaticos, B. and Badoual, M. (2020). Confinement Strategies in a Simple SIR Model. Regular and Chaotic dynamics, 25, 509-521.  

[14] Olanrewaju, R.O. (2018). On the Efficiency and Robustness of Commingle Wiener and Levy Driven Processes for Vasciek Model. World Academy of Science, engineering, and Technology (WASET): International Journal of Mathematics and Computational Sciences,12(11), 228-233. doi.org/10.5281/zendo.

How to cite this paper

Four-compartmental Epidemic and Endemic Dynamics Model for Delay Time  γΙ(t)-Distributed Existing Average

How to cite this paper: Rasaki Olawale Olanrewaju, Sodiq Adejare Olanrewaju, Oluwafemi Samson Balogun, Wasiu Adesoji Adepoju. (2023) Four-compartmental Epidemic and Endemic Dynamics Model for Delay Time  γΙ(t)-Distributed Existing Average. Journal of Applied Mathematics and Computation, 7(2), 267-279.

DOI: http://dx.doi.org/10.26855/jamc.2023.06.008

Home　|　Journals　|　Books　|　For Authors and Reviewers　|　Online Submission　|　Contact Us　|　About Us

Copyright © 2023 Hill Publishing Group Inc. All Rights Reserved.