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Reduction of discrete-time infectious disease models
  • Rafael Bravo de la Parra
Rafael Bravo de la Parra
Universidad de Alcala

Corresponding Author:rafael.bravo@uah.es

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In this work we propose the construction of discrete-time systems with two time scales in which infectious diseases dynamics are involved. We deal with two general situations. In the first, we consider that individuals affected by the disease move between generalized sites on a faster time scale than the dynamics of the disease itself. The second situation includes the dynamics of the disease acting faster together with another slower general process. Once the models have been built, conditions are established so that the analysis of the asymptotic behavior of their solutions can be carried out through reduced models. This is done using known reduction results for discrete-time systems with two time scales. These results are applied in the analysis of two new models. The first of them illustrates the first proposed situation, being the local dynamics of the SIS-type disease. Conditions are found for the eradication or global endemicity of the disease. In the second model, a case of co-infection with a primary disease and an opportunistic disease is treated, the latter acting faster than the former. Conditions for eradication and endemicity of co-infection are proposed.
03 Oct 2022Submitted to Mathematical Methods in the Applied Sciences
03 Oct 2022Submission Checks Completed
03 Oct 2022Assigned to Editor
14 Oct 2022Review(s) Completed, Editorial Evaluation Pending
14 Oct 2022Reviewer(s) Assigned
10 Feb 2023Editorial Decision: Revise Minor
14 Feb 20231st Revision Received
14 Feb 2023Submission Checks Completed
14 Feb 2023Assigned to Editor
14 Feb 2023Review(s) Completed, Editorial Evaluation Pending
18 Feb 2023Reviewer(s) Assigned
22 Feb 2023Editorial Decision: Accept