Bifurcation analysis of epidemic model waning immunity

Abstract

In this paper, we analyse the bifurcation of epidemic models. Those model is waning immunity. First, the stability of those system is analyzed by analyzing the stability of critical points. The threshold number that associated with the stability was determined. Later, the existence of bifurcation was analyzed. The result show that bifurcation exist and threshold number is considered as bifurcation parameter. Numerical simulation is given to confirm the analytical results by showing the graphic solutions and phase portrait.

Investigating the social dilemma of an epidemic model with provaccination and antivaccination groups: An evolutionary approach

“…Group behavior towards the provaccination or antivaccination groups was analyzed in [8] . The vaccination behavior of humans and the waning immunity effect in epidemic models were also analyzed in [4] , [6] , [10] , [18] .…”

“…However, in certain instances, the recovered individual relapse, a condition known as the waning of immunity. Exposed (E), quarantine (Q), hospitalized (H), and asymptomatic (A) compartments can be used in some epidemics to adequately examine disease dynamics [2] , [4] , [5] , [11] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] . An additional application of compartmental models in the research of disease transmission is the examination of supervision and moderation methods, such as immunization, and the impact of birthing and passing factors.…”

Influence of waning immunity on vaccination decision-making: A multi-strain epidemic model with an evolutionary approach analyzing cost and efficacy

“…In this investigation, we present a comprehensive behavioral epidemic model featuring multiple strains, built upon the SIRS/V dynamics and incorporating two distinct vaccination options. Our model allows individuals to make vaccination choices based on key factors such as the total number of infected individuals, vaccination costs, and the efficacy of available vaccines with the presence of wanning immunity ( Chun-Miin Chen, 2021 ; Fahdilla, Putri, & Haripamyu, 2021 ; Hamami, Cameron, Pollock, & Shankland, 2017 ; Nakata & Omori, 2015 ; Nishimura et al., 2023 ; Van Boven, De Melker, Schellekens, & Kretzschmar, 2000 ). The multistrain context enables an exploration of how these behavioral dynamics influence the dominance or coexistence of the two vaccination options over time ( Khan et al., 2022a , 2023 ; Rajib Arefin et al., 2019 ).…”