Mathematical modeling of COVID-19 with the effects of quarantine and detection

Abstract

In this paper, we focus on exploring a mathematical model that captures the dynamics of Corona Virus Disease (COVID-19), particularly emphasizing the influence of quarantine measures and the efficiency of detection and diagnosis protocols. Our study aims to comprehensively analyze the model, offering valuable insights and suggestions for effectively addressing the ongoing pandemic situation in various countries. The mathematical model under scrutiny is deterministic, and our approach involves a detailed examination of its equilibria. We rigorously employ methods to identify these points of equilibrium and subsequently undertake a thorough analysis of their stability. This analytical process is crucial in gaining a deeper understanding of the system’s behavior under various conditions, laying the foundation for informed recommendations to manage and mitigate the effects of the pandemic. To enhance the robustness of our findings, we complement our analytic results with numerical simulations. This multi-faceted approach allows us not only to understand the theoretical implications of the model but also to observe and validate its behavior in a simulated environment. The combination of mathematical analysis and numerical simulations strengthens the reliability and applicability of our results, contributing to a more comprehensive understanding of the dynamics at play in the context of COVID-19. Finally, we also discuss the optimal control approach in this paper to bound the epidemic.

Keywords

• Mathematical model
• COVID-19
• Stability
• Equilibrium points
• Routh–Hurwitz criteria
• Basic reproduction number