Babasola Oluwatosin, Kayode Oshinubi, Peter Olumuyiwa James, Onwuegbuche Faithful Chiagoziem, Oguntolu Festus Abiodun
Department of Mathematical Sciences, University of Bath, BA2 7AY, UK.
Universite Grenoble Alpes, France.
Inform Med Unlocked. 2022;35:101124. doi: 10.1016/j.imu.2022.101124. Epub 2022 Nov 8.
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.
新冠疫情是一场前所未有的全球健康危机，对世界人口和经济产生了巨大影响。许多科学家和研究人员共同努力，开发应对这一危机的方法，结果，研究人员已经开发出几种方法来理解新冠病毒的传播动态以及减轻其影响的方式。事实证明，实施数学模型有助于进一步了解相关行为，这有助于政策制定者采取必要的最佳政策来减少传播。大多数模型基于方程组，假定传播动态会瞬间变化。然而，据信新冠病毒在具有传播倾向之前有一个潜伏期。因此，为了充分捕捉动态，需要纳入延迟参数，该参数将考虑暴露个体在能够被感染之前的延迟。因此，在本文中，我们研究了具有凸发病率并结合时滞的SEIR传染病模型。我们首先将传染病模型作为经典常微分方程的形式进行讨论，然后纳入一个延迟来表示易感个体和暴露个体具有传染性的时期。其次，我们确定无病平衡点和地方病平衡点，并采用延迟微分方程稳定性理论研究它们的稳定性。此后，我们通过选择合适的参数进行数值模拟，以说明系统的理论结果，并更好地理解模型动态。我们还改变延迟的长度，以说明随着延迟参数的变化模型的变化，这使我们能够进一步深入了解动态系统中纳入延迟的影响。结果证实，纳入延迟会使系统不稳定，并迫使系统表现出振荡行为，从而导致周期解，这进一步帮助我们更深入地了解疾病的传播动态以及降低感染风险的策略。
