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An Integrable SIS Model on Time Scales

  • Martin BohnerEmail author
  • Sabrina Streipert
Conference paper
  • 59 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 312)

Abstract

In this work, we generalize the dynamic model introduced in Bohner and Streipert (Pliska Stud. Math. 26:11–28, 2016, [5]) 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, [5]) 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.

Keywords

Time scales Dynamic equations Difference equations Epidemiology Periodic solution Stability 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Missouri University of Science and TechnologyRollaUSA
  2. 2.Centre for Applications in Natural Resource MathematicsUniversity of QueenslandSt LuciaAustralia

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