A TRANSMISSION MODEL OF COVID-19 WITH QUARANTINE, TREATMENT AND VACCINATION
Abstract
A precise characterization of a Sars-Cov 2 dynamics transmission model with vaccination is presented. All the equilibria of the model as well as their stabilities have been described by use of algebraic geometry approach. The model analysis shows that the combined use of the quarantine and treatment strategy with a vaccination strategy may lead to the effective disease control or elimination.
References
[1]W. W. Adams and P. Loustaunau, An introduction to Gröebner bases, Volume 3 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, (1994), 301.
[2]Y. Amin, J. Hadi and B. Stelios, Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak, Chaos, Solitons and Fractals 136 (2020), 109883.
[3]S. Basu, R. Pollack and M.-F. Roy, Algorithms in real algebraic geometry, Volume 10 of Algorithms and Computation in Mathematics, Springer-Verlag, Berlin, 2nd ed., 2006, p. 662.
[4]T. Becker and V. Weispfenning, In cooperation with Heinz Kredel, Gröebner bases, A computational approach to commutative algebra, Volume 141 of Graduate Texts in Mathematics, Springer-Verlag, New York, 1993, p. 581.
[5]L. Billings, A. Fiorillo and I. B. Schwartz, Vaccinations in disease models with antibody-dependent enhancement, Math. Biosci. 211(2) (2008), 265-281.
[6]C. W. Brown, M. El Kahoui, D. Novotni and A. Weber, Algorithmic methods for investigating equilibria in epidemic modeling, J. Symbolic Comput. 41(11) (2006), 1157-1173.
[7]D. Cox, J. Little and D. O’Shea, Ideals, varieties, and algorithms, Undergraduate Texts in Mathematics, Springer, New York, 3d ed., 2007.
[8]M. El Kahoui and A. Otto, Stability of disease free equilibria in epidemiological models, Mathematics in Computer Science, Birkhauser Verlag Basel, Switzerland, 2 (2009), 517-533.
[9]N. Ferguson, R. Anderson and S. Gupta, The effect of antibody-dependant enhancement on the transmission dynamics and persistence of multiple strain pathogens, Proc. Natl. Acad. Sci. USA 96 (1999), 790-794.
[10]A. Otto and M. Amidou, A transmission model of Covid-19 with quarantine and treatment, Far East Journal of Applied Mathematics 108(2) (2020), 113-128.
[11]P. van den. Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29-48.
[12]S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos, Volume 2 of Texts in Applied Mathematics. Springer-Verlag, New York, 2nd ed., 2003, 864.