A two diffusion stochastic model for the spread of the new corona virus SARS-CoV-2

Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CоV-2

“…The virus remains persistent in population if at least one of the classes of symptomatic infectious, asymptomatic infectious, hospitalized infectious or super-spreader is not empty. From the mathematical point of view, in accordance with [19], we say that system (1) is persistent in mean if lim t→∞ 1 t t 0 (I(s) + P(s) + A(s) + H(s)) ds > 0, P − a.s. .…”

“…In this paper we observe the SEIPHAR epidemic model for modeling the spread of the new corona virus SARS-CoV-2, introduced in the recent paper [19]. They assumed that the human population is divided into seven mutually exclusive compartments:…”

“…Value Units Λ Estimated daily number of newborns in Wuhan in 2019 310 [20] Existence and uniqueness of a positive global solution of system of stochastic differential equations (1) is proven in [19].…”

“…Remark 2.1. According to [19], note that the set Γ = {(S(t), E(t), I(t), P(t), H(t), A(t), R(t)) : S(t) > 0, E(t) > 0, I(t) > 0, P(t) > 0, H(t) > 0, A(t) > 0, R(t) > 0, N(t) ≤ Λ/µ is a positively invariant set of the system (1) for every t > 0, i.e. if the system starts from Γ , it never leaves Γ .…”

“…In Section 4, the sufficient conditions for extinction and persistence of the disease are establish. In addition to the results proven in [19], we have introduced a threshold parameter R S 0 , the counterpart of the basic reproduction number, which can be used to utilize in identifying the stochastic extinction and persistence for the stochastic epidemic model. In Section 5, reproduction numbers for deterministic and corresponding stochastic epidemic models for the spread of SARS-CoV-2 virus are compared.…”