Reduction of discrete-time infectious disease models
- Rafael Bravo de la Parra
Abstract
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