Time-delayed models of infectious diseases dynamics

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Okonna, Ime Udo;
(2018)
  • Subject: QA299 | RC0109

This research work is on time-delayed models of infectious diseases dynamics. The dynamics of\ud infectious diseases are studied in the presence of time delays representing temporary immunity or\ud latency. We have designed and analysed time-delayed models with various ... View more
  • References (10)

    2.4 Disease Free Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Basic Reproduction Number . . . . . . . . . . . . . . . . . . . . . . 24 2.6 Local Stability of the Disease Free Equilibrium . . . . . . . . . . . . 26 2.7 Global Stability of the Disease Free Equilibrium . . . . . . . . . . . 29 2.8 Local Stability of the Endemic Equilibrium . . . . . . . . . . . . . . 33 2.9 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    3 Two-Infection Mathematical Model with Time Delay 46 3.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2 Positivity of Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3 Steady States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.4 Basic Reproduction Number . . . . . . . . . . . . . . . . . . . . . . 56 3.5 Local Stability of Disease Free Equilibrium . . . . . . . . . . . . . . 58 3.6 Local Stability of the Endemic Equilibrium . . . . . . . . . . . . . . 61 3.7 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

    4 Latency Model with Saturated Incidence Rate 79 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2 Derivation of the Model . . . . . . . . . . . . . . . . . . . . . . . . 80 4.3 Steady States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    [1] W. O. Kermack and A. G. McKendrick, A Contribution to the Mathematical Theory of Epidemics I, Proceedings of the Royal Society Series A, Vol. 115, No. 772, (1927), pp.700-721.

    [2] W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics. II. The problem of endemicity, Proceedings of the Royal Society of London. Series A 138(834) (1932) 55{83.

    [3] W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics. III. Further studies of the problem of endemicity, Proceedings of the Royal Society of London. Series A 141(843) (1933) 94{122.

    [4] E. Thomas, Applied Delay Di erential Equations, Surveys and Tutorials in the Applied Mathematical Sciences Volume 3, Springer, (2009).

    [8] E. Beretta, Y. Takeuchi, Convergence results in SIR epidemic mode1 with varying population sizes, Nonlinear Anal. 28 (1997) 1909{ 1921.

    [22] R. Ross, The Prevention of Malaria, 2nd ed., Jhon Murray, London, 1911 [69] R. D. Driver, Ordinary and Delay Di erential Equations, Springer-Verlag, New York, 1977

    [71] N. G. Chebotarev and N. N. Meiman, The Routh-Hurwitz problem for polynomials and entire functions, Trudy Mat. Inst. Steklov., 26, Acad. Sci. USSR, Moscow{Leningrad, 1949, 332 pp

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