Session S25 - New Methods and Emerging Applications in Dynamics, Networks, and Control

Monday, July 12, 18:35 ~ 19:05 UTC-3

Simple models for complex realities: The case of COVID-19.

Fernando Córdova Lepe

Universidad Católica del Maule, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In the differential models construction processes, as instruments for the decision-making, there is a need for a detailed structuring of the reference system, for example, incorporating a large number of variables, specific functional relationships, and precision in the parameters. However, these are supported by more elementary models that capture essential general patterns of the phenomenon; it is the role that the SEIR model has played for the epidemiological analysis of Covid-19. In its version with constant parameters, this base model presents strong resistance to its generalizations to attempts to break the unimodal behavior of the epidemic curve. The main objective of the presentation is to propose a new basic model or "toy model," which is still a generalization to the classic SEIR, that incorporating the concepts of "reaction rate" and "restitution rate" associated with the rate transmission, overcomes the limitation by incorporating the possibility of multiple oscillatory modes that geometrically correlate with the existing data that the pandemic has left for various countries or territories. Also, some related mathematical challenges and other epidemiological considerations are detailed.

Córdova-Lepe, F.; Robledo, G.; Vergaño-Salazar, J.G. (2020) Mitigation effort performance index and bounds for inflection points of the epidemic curve. Supplies to fight COVID-19. Submitted.

Cabrera, M; Córdova-Lepe, F; Gutiérrez-Jara, JP; Vogt-Geisse, K. (2020) An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors. Submitted.

Córdova-Lepe, F; Vogt-Geisse, K. (2021) A dynamic law for the contagion rate in SIR-type models. To be submitted.

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