A model for the dynamics of COVID-19 infection transmission in human with latent delay

TL;DR

This paper develops a delay differential equation model for COVID-19 infection within humans, incorporating latent and immune response delays, and analyzes how these delays affect disease stability and dynamics.

Contribution

It introduces a novel mathematical model with delay parameters for COVID-19 within-human transmission, analyzing stability and bifurcations due to these delays.

Findings

Latent delay stabilizes disease dynamics.

Immune response delay destabilizes the system.

Hopf bifurcation indicates oscillatory behavior.

Abstract

In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a 'latent period' and 'the time for immune response' as delay parameters, allowing us to study the effects of time delays in human COVID-19 infection. We have determined the equilibrium points and analyzed their stability. The disease-free equilibrium is stable when the basic reproduction number, $R_0$, is below unity. Stability switch of the endemic equilibrium occurs through Hopf-bifurcation. This study shows that the effect of latent delay is stabilizing whereas immune response delay has a destabilizing nature.