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Analysis of Stability and Sensitivity of Deterministic and Stochastic Models for the Spread of the New Corona Virus SARS-CoV-2

Basic reproduction number for deterministic SEIPHAR model and its stochastic counterpart for the spread of SARS-CoV-2 virus are analyzed and compared. For deterministic version of the model, conditions for stability of the disease- free equilibrium are derived and, in addition, conditions for existence of bifurcation state related to endemic equilibrium are established. For stochastic model, conditions for extinction and persistence in mean of the disease are derived. Complete sensitivity analysis of thresholds between the extinction and mean- persistence are performed for both the deterministic and the stochastic version of the model. Influence of variation in parameter values is illustrated for epidemics in Wuhan in early 2020.

SARS-CoV-2 virus epidemic model ; basic reproduction number ; disease-free equilibrium ; endemic equilibrium ; stability ; bifurcation ; stochastic differential equation (SDE) ; Brownian motion ; extinction ; persistence

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