Computational and Mathematical Biophysics (Jun 2024)
Stability and bifurcation analysis of a nested multi-scale model for COVID-19 viral infection
Abstract
In this study, a nested multi-scale mathematical model is proposed and studied for COVID-19 viral infection. The well-posedness of the multi-scale model is discussed, followed by the stability analysis of the equilibrium points. The proposed model admits two equilibrium solutions: the infection-free equilibrium and the infected equilibrium. The infection-free equilibrium point is shown to be globally asymptotically stable provided that the value of the basic reproduction number is less than unity. When the value of the basic reproduction number exceeds unity, a unique infected equilibrium exists, and the system is found to undergo a forward (trans-critical) bifurcation. Two-parameter heat plots are performed to identify the parameter combinations for the stability of the admitted equilibrium points. From the sensitivity analysis, the transmission rate, infection rate, and birth rate were found to be most sensitive to the basic reproduction number. The influence of the within-host sub-model parameters on the between-host sub-model variables is numerically illustrated. The spread of infection in a community is shown to be influenced by the within-host sub-model parameters, such as the production of viral particles, the clearance rate of infected cells by the immune system, and the clearance rate of viral particles by the immune system. The comparative effectiveness of three health interventions (antiviral drugs, immunomodulators, and generalized social distancing) for COVID-19 infection is examined using the reproductive number as an indicator of the effectiveness of these interventions. The results from the comparative effectiveness study suggest that a combined strategy of antiviral drugs, immunomodulators, and generalized social distancing would be the best strategy to implement to contain the spread of infection in the community.
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