The Dynamic Analysis of the COVID-19 Spread Model in the SIHCR Population with Time Delay

DOI

10.2991/978-94-6463-148-7_35How to use a DOI?

Keywords

Mathematical Model of SIHCR; Dynamic Analysis; Basic Reproduction Number; Time Delay

Abstract

This study discusses the dynamic analysis of the COVID-19 spread model in the SIHCR population with time delay to represent the behavior of the spread of COVID-19 with time delay. The SIHCR model divides the human population into five subpopulations, namely Susceptible S , Infected I , Hospitalized H , Critical C , and Recovered R . The dynamic analysis is carried out by determining the equilibrium point, the basic reproduction number R 0 , and stability analysis of the equilibrium point. The result of this study is two equilibrium points, namely the disease-free equilibrium point E 0 and the endemic equilibrium point E 1 . Then the basic reproduction number R 0 was calculated using the given parameters and produce the value R 0 > 1 . The stability analysis can be obtained by linearization around the equilibrium points. The disease-free equilibrium point is unstable and the endemic equilibrium point is locally asymptotically stable. Next, simulation of the SIHCR model with and without time delay was carried out under disease-free and endemic conditions. Simulations are carried out using variations in the value of the delay time to determine the dynamic behavior of the model. In disease-free and endemic conditions, it shows differences in the dynamic behavior of the model. The smaller the delay time, the condition is almost the same as the SIHCR model without time delay towards stability. Meanwhile, the greater the delay time, the longer the SIHCR model leads to stability. So it can be concluded that the time delay affects the stability of the SIHCR model.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Ifa Sarifatus Hidayati
AU  - Ari Kusumastuti
AU  - Heni Widayani
PY  - 2023
DA  - 2023/05/29
TI  - The Dynamic Analysis of the COVID-19 Spread Model in the SIHCR Population with Time Delay
BT  - Proceedings of the 12th International Conference on Green Technology (ICGT 2022)
PB  - Atlantis Press
SP  - 352
EP  - 367
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6463-148-7_35
DO  - 10.2991/978-94-6463-148-7_35
ID  - Hidayati2023
ER  -