A study on COVID-19 transmission dynamics: stability analysis of SEIR model with Hopf bifurcation for effect of time delay

Abstract

This paper deals with a general SEIR model for the coronavirus disease 2019 (COVID-19) with the effect of time delay proposed. We get the stability theorems for the disease-free equilibrium and provide adequate situations of the COVID-19 transmission dynamics equilibrium of present and absent cases. A Hopf bifurcation parameter τ concerns the effects of time delay and we demonstrate that the locally asymptotic stability holds for the present equilibrium. The reproduction number is brief in less than or greater than one, and it effectively is controlling the COVID-19 infection outbreak and subsequently reveals insight into understanding the patterns of the flare-up. We have included eight parameters and the least square method allows us to estimate the initial values for the Indian COVID-19 pandemic from real-life data. It is one of India’s current pandemic models that have been studied for the time being. This Covid19 SEIR model can apply with or without delay to all country’s current pandemic region, after estimating parameter values from their data. The sensitivity of seven parameters has also been explored. The paper also examines the impact of immune response time delay and the importance of determining essential parameters such as the transmission rate using sensitivity indices analysis. The numerical experiment is calculated to illustrate the theoretical results.

Dynamics of an SEIRS COVID-19 Epidemic Model with Saturated Incidence and Saturated Treatment Response: Bifurcation Analysis and Simulations

“…We proved that the inclusion of both saturated incidence and saturated treatment is also a cause of Hopf bifurcation. This is a topic of research that has been scarcely studied for the dynamics of COVID-19 (see, e.g., the analysis of delay-induced Hopf bifurcation in [29] and [30]) and has important implications for epidemic control, because this type of bifurcation can produce oscillatory patterns in the number of infected individuals. Further research should still be made to improve our understanding of the different dynamics that can occur in this epidemic outbreak.…”

Backward and Hopf bifurcation analysis of an SEIRS COVID-19 epidemic model with saturated incidence and saturated treatment response

“…We proved that the inclusion of both saturated incidence and saturated treatment is also a cause of Hopf bifurcation. This is a topic of research that has been scarcely studied for the dynamics of COVID-19 (see, e.g., the analysis of delay-induced Hopf bifurcation in [1] and [25]) and has important implications for epidemic control, because this type of bifurcation can produce oscillatory patterns in the number of infected individuals. Further research should still be made to improve our understanding of the different dynamics that can occur in this epidemic outbreak.…”

Analysis of Non-Pharmaceutical Interventions Impacts on COVID-19 Pandemic in Iran

“…Jayrold et al [25] Used the extension of SEIR to estimate the effective reproduction number for several countries. [26] Developed a SEIR model with the effect of time delay for India. Arghya et al…”

“…Jayrold et al [25] Used the extension of SEIR to estimate the effective reproduction number for several countries. [26] Developed a SEIR model with the effect of time delay for India. Arghya et al [27] applied SEIR epidemiological model to predict the peak of infected cases and explore the impact of social distancing and testing-quarantining on virus propagation.…”