Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate

Oluwatosin Babasola, Oshinubi Kayode, Olumuyiwa James Peter, Faithful Chiagoziem Onwuegbuche, Festus Abiodun Oguntolu

Research output: Contribution to journalReview articlepeer-review

12 Citations (SciVal)


COVID-19 pandemic represents an unprecedented global health crisis which has an enormous impact on the world population and economy. Many scientists and researchers have combined efforts to develop an approach to tackle this crisis and as a result, researchers have developed several approaches for understanding the COVID-19 transmission dynamics and the way of mitigating its effect. The implementation of a mathematical model has proven helpful in further understanding the behaviour which has helped the policymaker in adopting the best policy necessary for reducing the spread. Most models are based on a system of equations which assume an instantaneous change in the transmission dynamics. However, it is believed that SARS-COV-2 have an incubation period before the tendency of transmission. Therefore, to capture the dynamics adequately, there would be a need for the inclusion of delay parameters which will account for the delay before an exposed individual could become infected. Hence, in this paper, we investigate the SEIR epidemic model with a convex incidence rate incorporated with a time delay. We first discussed the epidemic model as a form of a classical ordinary differential equation and then the inclusion of a delay to represent the period in which the susceptible and exposed individuals became infectious. Secondly, we identify the disease-free together with the endemic equilibrium state and examine their stability by adopting the delay differential equation stability theory. Thereafter, we carried out numerical simulations with suitable parameters choice to illustrate the theoretical result of the system and for a better understanding of the model dynamics. We also vary the length of the delay to illustrate the changes in the model as the delay parameters change which enables us to further gain an insight into the effect of the included delay in a dynamical system. The result confirms that the inclusion of delay destabilises the system and it forces the system to exhibit an oscillatory behaviour which leads to a periodic solution and it further helps us to gain more insight into the transmission dynamics of the disease and strategy to reduce the risk of infection.

Original languageEnglish
Article number101124
JournalInformatics in Medicine Unlocked
Early online date8 Nov 2022
Publication statusPublished - 31 Dec 2022

Bibliographical note

Funding Information:
The first author acknowledge the support of the ESPRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa) , under the project EP/L015684/1 . The fourth author also acknowledge the Science Foundation Ireland through the SFI Centre for Research Training in Machine Learning ( 18/CRT/6183 ).


  • Convex incidence rate
  • COVID-19
  • Delay differential equation
  • SEIR epidemic model
  • Stability

ASJC Scopus subject areas

  • Health Informatics


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