An Integrable SIS Model on Time Scales
In this work, we generalize the dynamic model introduced in Bohner and Streipert (Pliska Stud. Math. 26:11—28, 2016, ) in the context of epidemiology. This model exhibits many similarities to the continuous susceptible-infected-susceptible model and is therefore of particular interest to formulate a generalization of a continuous model on time scales. In this work, we extend the results in Bohner and Streipert (Pliska Stud. Math. 26:11—28, 2016, ) for time-dependent coefficients rather than constant parameters and derive an explicit solution. We further discuss the stability of periodic solutions for the corresponding discrete model with periodic coefficients. We conclude the analysis of the SIS model by considering time-dependent vital dynamics and derive its explicit solution on a general time scale.
M. Bohner and S. Streipert, "An Integrable SIS Model on Time Scales," Springer Proceedings in Mathematics and Statistics, vol. 312, pp. 187-200, Springer, Feb 2020.
The definitive version is available at https://doi.org/10.1007/978-3-030-35502-9_7
24th International Conference on Difference Equations and Applications, ICDEA 2018 (2018: May 21-24, Dresden, Germany)
Mathematics and Statistics
Keywords and Phrases
Difference equations; Dynamic equations; Epidemiology; Periodic solution; Stability; Time scales
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Article - Conference proceedings
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01 Feb 2020