A delayed deterministic and stochastic SIRICV model: Hopf bifurcation and stochastic analysis

Youssra Hajri, Amina Allali and Saida Amine

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 215, issue C, 98-121

Abstract: In this paper, we present a delayed deterministic and stochastic SIRICV models to investigate the effects of the white noise intensities and the waning immunity of vaccinated individuals in the evolution of the disease. For the deterministic SIRICV model, the basic reproduction number R0 and the equilibrium points are calculated. The local stability of equilibrium points is analyzed. Particularly, when R0<1 the disease-free equilibrium is locally stable for any positive value of τ. Furthermore, when R0>1, the local stability and sufficient conditions to ensure the occurrence of Hopf bifurcation for the endemic equilibrium point are established by considering the time delay τ as a bifurcation parameter. For the stochastic SIRICV model, the conditions of the extinction and persistence of the disease are given by using the stochastic basic reproduction numbers R0s and R0s∗. Numerical simulations are presented to enhance our analytical results and contrast the deterministic and stochastic models.

Keywords: Deterministic epidemic SIRICV model; Weak-immunity; Hopf bifurcation; Stochastic epidemic SIRICV model; Extinction; Persistence (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:215:y:2024:i:c:p:98-121

DOI: 10.1016/j.matcom.2023.07.027

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