Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

Consider the heterogeneity(e.g.,heterogeneous social behaviour,heterogeneity due to different geography,contrasting contact patterns and different numbers of sexual partners etc.)of host population,in this paper,the authors propose an infection age multigroup SEIR epidemic model.The model system also incorporates the feedback variables,where the infectivity of infected individuals may depend on the infection age.In the direction of mathematical analysis of model,the basic reproduction number R_0 has been computed.The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R_(0).More precisely,for R_(0)≤1,the disease-free equilibrium is globally asymptotically stable and for R_(0)>1,they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method.By considering a numerical example,they investigate the effects of infection age and feedback on the prevalence of the disease.Their result shows that feedback parameters have different and even opposite effects on different groups.However,by choosing an appropriate value of feedback parameters,the disease could be eradicated or maintained at endemic level.Besides,the infection age of infected individuals may also change the behaviour of the disease,global stable to damped oscillations or damped oscillations to global stable.

SIVS EPIDEMIC MODELS WITH INFECTION AGE AND NONLINEAR VACCINATION RATE

Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.

THE DYNAMICS OF A DISCRETE SEIT MODEL WITH AGE AND INFECTION AGE STRUCTURES

Age and infection age have significant influence on the transmission of infectious dis- eases, such as HIV/AIDS and TB. A discrete SEIT model with age and infection age structures is formulated to investigate the dynamics of the disease spread. The basic reproduction number R0 is defined and used as the threshold parameter to character- ize the disease extinction or persistence. It is shown that the disease-free equilibrium is globally stable if R0 〈 1, and it is unstable if R0 〉 1. When R0 〉 1, there exists an endemic equilibrium, and the disease is uniformly persistent. The stability of the endemic equilibrium is investigated numerically.

Global dynamics of an age-structured viral infection model with general incidence function and absorption

In this paper, we propose an age-structured viral infection model with general incidence function that takes account of the loss of viral particles due to their absorption into susceptible cells. The proposed model is described by partial differential and ordinary differential equations. We first show that the model is mathematically and biologically well-posed. Furthermore, the uniform persistence and the global behavior of the model are investigated. Moreover, the age-structured models and results presented in many previous studies are improved and generalized.

A CLASS OF SIS EPIDEMIC MODEL WITH SATURATION INCIDENCE AND AGE OF INFECTION

Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynamical behavior of this model and define the basic reproductive number R0. The authors also prove that the diseased-free equilibrium is globally asymptotically stable if R0 〈 1. The endemic equilibrium is locally asymptotically stable if K1 〉 α and R0 〉 1.

GLOBAL STABILITY OF AN AGE-STRUCTURED SIR EPIDEMIC MODEL WITH PULSE VACCINATION STRATEGY

This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age （duration since infection）. The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infectiomfree situation if the impulsive period T and proportion p satisfy Ro（p,T） 〈 1. Optimal problem is discussed： Pulse vaccination strategy with minimal costs at given R0（p, T） 〈 1.

The relationship between controllability, optimal testing resource allocation, and incubation-latent period mismatch as revealed by COVID-19

The severe shortfall in testing supplies during the initial COVID-19 outbreak and ensuing struggle to manage the pandemic have affirmed the critical importance of optimal supplyconstrained resource allocation strategies for controlling novel disease epidemics.To address the challenge of constrained resource optimization for managing diseases with complications like pre-and asymptomatic transmission,we develop an integro partial differential equation compartmental disease model which incorporates realistic latent,incubation,and infectious period distributions along with limited testing supplies for identifying and quarantining infected individuals.Our model overcomes the limitations of typical ordinary differential equation compartmental models by decoupling symptom status from model compartments to allow a more realistic representation of symptom onset and presymptomatic transmission.To analyze the influence of these realistic features on disease controllability,we find optimal strategies for reducing total infection sizes that allocate limited testing resources between‘clinical’testing,which targets symptomatic individuals,and‘non-clinical’testing,which targets non-symptomatic individuals.We apply our model not only to the original,delta,and omicron COVID-19 variants,but also to generically parameterized disease systems with varying mismatches between latent and incubation period distributions,which permit varying degrees of presymptomatic transmission or symptom onset before infectiousness.We find that factors that decrease controllability generally call for reduced levels of non-clinical testing in optimal strategies,while the relationship between incubation-latent mismatch,controllability,and optimal strategies is complicated.In particular,though greater degrees of presymptomatic transmission reduce disease controllability,they may increase or decrease the role of nonclinical testing in optimal strategies depending on other disease factors like transmissibility and latent period length.Importantly,our model allows a spectrum of diseases to be compared within a consistent framework such that lessons learned from COVID-19 can be transferred to resource constrained scenarios in future emerging epidemics and analyzed for optimality.