Analysis of Dynamics of Recurrent Epidemics: Periodic or Non-periodic

Sufficient reproduction numbers to prevent recurrent epidemics

“…Projections are made under the assumption of gamma-distributed generation times (with an average of 5.2 days and a standard deviation of 1.7 days) and a total duration of the infection of 11.7 days, inclusive of the latent phase (corresponding to the parameterization for the ancestral strain of SARS-CoV-2; see Table 1). (Cori et al, 2013;Liu et al, 2018;Gostic et al, 2020;Zhang et al, 2020;Cereda et al, 2021;Trevisin et al, 2023), we adopt a susceptible-infected-removed model with age-of-infection structure (Kermack and McKendrick, 1927;Cao et al, 2019) and discretize it in time and age of infection (Allen and van den Driessche, 2008), thereby obtaining an epidemiological projection matrix that can be used to simulate the transmission process. The projection matrix can be made time-or policy-dependent by substituting the basic RN with the effective or control RNs (Materials and Methods).…”

“…Therefore, preventing pathogens from even temporarily spreading within a population gains importance because case imports are often unavoidable, as testified, for example, by MERS-CoV outbreaks in the Middle East (Gardner and MacIntyre, 2014) or measles in the US that occur despite control efforts (Blumberg et al, 2015). The issue of recurrent epidemics has been explored via deterministic and stochastic models, which have highlighted their various features, often concentrating on seasonal dynamics (Johansen, 1996; Finkenstädt et al, 2002; Stone et al, 2007; Begon et al, 2009; Zheng et al, 2015; Cao et al, 2019; Saad-Roy et al, 2020).…”

Bifurcation analysis of an age‐structured epidemic model with two staged‐progressions

“…1,[7][8][9][10][11] In addition to global stability, the destabilization of age-dependent positive steady state has attracted great attention recently, which may result in bifurcation behaviors. [12][13][14][15][16][17][18][19] To conduct analysis, the age-structured model can be rewritten as abstract Cauchy problem with a Lipschitz perturbation of a closed linear operator that is non-densely defined but satisfies the estimates of Hille-Yosida theorem. Due to the age-dependent parameters or infectious delay, Hopf bifurcation occurs in the population dynamics.…”

“…Due to the age-dependent parameters or infectious delay, Hopf bifurcation occurs in the population dynamics. In other studies, 15,18,19 epidemic models with age structure were proposed for recurrent diseases by incorporating temporary immunity, allowing the transition between periodic and non-periodic behaviors of the disease. In consideration of differential infectivity with age of infection in infectious class, compartmental models for pest-pathogen, predator-prey, and virus infections were studied in other studies, [12][13][14]17 and bifurcation results were established when the disease is being persistent.…”

“…Denoting a 0 = 𝜏, here 𝜏 is the critical infection age that when the acute period exceeds 𝜏, then the chronic stage begins, which is different from the infectious delay in other studies. 15,18,19 The susceptible population is assumed to experience logistic growth with b and K being intrinsic growth rate and carrying capacity. 𝜇, 𝛼(a), and 𝜖 represent natural death rate, disease-induced death rate, and the rate of transfer from acute to chronic infection, respectively.…”