International Journal of Mathematics Trends and Technology
Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P501
In this paper, we proposed a fractional SVIR order model to study the transmission dynamics of Chickenpox. We showed the existence of the equilibrium states. The basic reproduction number of the model was evaluated in terms of parameters in the model using the next generation matrix approach. We provided the conditions for the stability of the disease-free and the endemic equilibrium points. Also a detailed stability analysis of the model was carried out. Also, numerical simulations of the model were carried out using Adams-type predictor-corrector method and the paper provided a theoretical basis to control the spread of Chickenpox.
[1] N. M. Furguson,R. M. Anderson and G. P. Garnett, "Mass vaccination to control chicken- pox: The in uence of zoster," Medicinal sciences, vol. 93, pp. 7231-7235, 1996.
[2] O. Forde and J.A.P Meeker , "Mathematical model on the transmission dynamics of Veri- cella with treatment," Journal of Mathematical biology, no. 2, pp. 265-382, 2010.
[3] E. Berretta and V. Capasso, "On the general structure of the epidemic system:Global asymptotic stability," Comp. and Maths. with Appls., no. 12A, pp. 677-694, 1986.
[4] W. O. Kermack and A. G. Mckendrick, "Contributions to the mathematical theory of epidemics, part 1," Proceedings of the Royal Society of Edinburgh, vol. 115, pp. 700-721, 1927.
[5] J. Li and X. Zou, "Generalization of the Kermack-Mckendrick SIR Model to a Patchy Environment for a disease with Latency," vol. 4, no. 2, pp. 92-118, 2009.
[6] Nnaemeka S. A., and Amanso O., "Analysis of a model on the transmission dynamics (with prevention and control) of Hepatitis B", Journal of Fractional Calculus and Application, Vol. 12(1), pp. 76-89, 2021.
[7] Gonza, L.P., Arenas, J. A., and Chen-Chapentier B. "A Fractional order Epidemic Model for the Simulation of outbreaks of in uenza (HINI). Mathematical Methods in the Applied Sciences" , 2218-2226, 2014.
[8] Petras, I. Fractional Order non linear systems: Modelling, analysis and Simulation. Springer Verley, 2011.
[9] E. Ahmed, A. M. A. El-Sayed and H. A. A. El-Saka, "Equilibrium points,stability and numerical solutions of fractional-order predator-prey and rabies models," J. Math. Anal. Appl., no. 325, pp. 542-553, 2007.
[10] I. Area, H. Batar, J. Losada, JJ Nieto, M. Shammakh and A. Torres, "On a fractional order ebola epidemic model," Advances in Dierence Equations, p. 278, 2015.
[11] K. Diethelm, "A fractional calculus based model for the simulation of an outbreak of dengue fever," Nonlinear Dynamics, vol. 71, no. 4, pp. 613-619, 2011.
[12] T. Sardar, S. Rana, S. Bhattacharya, K. Al-Khaled and J. Chattopadhyay, "A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector," Mathematical Biosciences, no. 263, pp. 18-36, 2015.
[13] I. Podlubny, Fractional Dierential Equations, Academic Press, 1999.
[14] R. Gorenglo, J. Loutchko and Y. Luchko, "Computation of the Mittag-Leer function and its derivative," Fractional Calculus and Applied Analysis, vol. 5, no. 4, pp. 491-518, 2002.
[15] Aguegboh, N.S., Nwokoye, N.R., Onyiaji, N.E., Amanso, O.R. and Oranugo, D.O. (2020) A Fractional Order Model for the Transmission Dynamics of Measles with Vaccination. Open Access Library Journal , 7: e6670. https://doi.org/10.4236/oalib 1106670.
Aguegboh,Nnaemeka S,Uko Ofe,Netochukwu E. Onyiaji,Ugwu O. Lovelyn, "Fractional Model on the Dynamics of Chicken Pox with Vaccination," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 1-14, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P501
PDF 
Abstract 
Keywords 
References 
Citation