Analysis Time-Delayed SEIR Model with Survival Rate for COVID-19 Stability and Disease Control

M. H. Hassan (), Tamer El-Azab, Ghada AlNemer, M. A. Sohaly and H. El-Metwally
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M. H. Hassan: October High Institute for Engineering and Technology, Giza 12596, Egypt
Tamer El-Azab: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Ghada AlNemer: Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
M. A. Sohaly: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
H. El-Metwally: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2024, vol. 12, issue 23, 1-16

Abstract: This paper presents a mathematical model to examine the transmission and stability dynamics of the SEIR model for COVID-19. To assess disease progression, the model incorporates a time delay for the time delay and survival rates. Then, we use the Routh–Hurwitz criterion, the LaSalle stability principle, and Hopf bifurcation analysis to look at disease-free and endemic equilibrium points. We investigate global stability using the Lyapunov function and simulate the model behavior with real COVID-19 data from Indonesia. The results confirm the impact of time delay on disease transmission, mitigation strategies, and population recovery rates, demonstrating that rapid interventions can significantly impact the course of the epidemic. The results indicate that a balance between transmission reduction and vaccination efforts is crucial for achieving long-term stability and controlling disease outbreaks. Finally, we estimate the degree of disease control and look at the rate of disease spread by simulating the genuine data.

Keywords: SEIR model; delay differential equations; stability analysis; Hopf bifurcation; Lyapunov function; COVID-19 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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