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SUMMARY The poultry-housing environment plays a significant role in the transmission and persistence of the egg-associated pathogen Salmonella Enteritidis in laying flocks. The commercial egg industry is in the midst of a transition toward cage-free housing, but the food safety ramifications of this shift are not yet certain. The present study assessed internal organ colonization by Salmonella Enteritidis in layer pullets reared in cage-free housing and infected at two different ages. Groups of 280 pullets were transferred from the rearing facility (at 9 wk of age in one trial and 15 wk in another) to a containment facility with four isolation rooms simulating commercial cage-free barns with perches and nest boxes (70 birds/room). Twenty-four pullets in each room were orally inoculated with Salmonella Enteritidis immediately after placement in the containment facility. At 1–2 wk postinoculation in each trial, samples of liver, spleen, and intestinal tract were collected from all birds in two rooms for bacteriologic culturing to detect Salmonella Enteritidis. At 21–22 wk of age, samples of spleen, ovary, and intestinal tract were similarly collected and tested from all birds in the remaining two rooms. Among samples collected at 1–2 wk postinoculation, Salmonella Enteritidis was isolated significantly more often from groups of pullets infected initially at 15 wk of age than from those infected at 9 wk (61% vs. 38% of livers, 59% vs. 31% of spleens, and 84% vs. 57% of intestines). Among samples collected at 21–22 wk of age, the frequency of recovery of Salmonella Enteritidis was again significantly greater in birds infected at 15 wk of age than in those infected at 9 wk (16% vs. 6% of spleens, 9% vs. 1% of ovaries, and 26% vs. 10% of intestines). These data suggest that Salmonella Enteritidis infections introduced into flocks during the later stages of pullet rearing have greater potential to persist into the early phase of egg production. RESUMEN Nota de investigación- Colonización de órganos internos por Salmonella Enteritidis en pollitas de postura infectadas en dos edades diferentes durante la crianza en alojamiento sin jaulas. El ambiente en alojamientos avícolas juega un papel importante en la transmisión y persistencia del patógeno asociado a los huevos Salmonella Enteritidis en parvadas postura. La industria comercial del huevo se encuentra en medio de una transición hacia alojamientos sin jaulas, pero las ramificaciones de este cambio en la seguridad alimentaria aún no están determinadas. El presente estudio evaluó la colonización de órganos internos por Salmonella Enteritidis en pollitas de postura criadas en alojamientos sin jaulas e infectadas a dos edades diferentes. Se transfirieron grupos de 280 pollitas desde las instalaciones de cría (a las 9 semanas de edad en un ensayo y a las 15 semanas en un segundo ensayo) a una instalación de contención con cuatro salas de aislamiento que simulaban alojamientos comerciales sin jaulas con perchas y nidos (70 aves/sala). Veinticuatro pollitas en cada sala fueron inoculadas oralmente con Salmonella Enteritidis inmediatamente después de su colocación en la instalación de contención. En cada ensayo, de una a dos semanas después de la inoculación, se recolectaron muestras de hígado, bazo y tracto intestinal para cultivo bacteriológico de todas las aves en dos salas para detectar Salmonella Enteritidis. A las 21-22 semanas de edad, se recolectaron y analizaron de manera similar muestras de bazo, ovario y tracto intestinal de todas las aves en las dos salas restantes. Entre las muestras recolectadas entre una y dos semanas después de la inoculación, Salmonella Enteritidis se aisló significativamente con mayor frecuencia en grupos de pollitas infectadas inicialmente a las 15 semanas de edad que en aquellas infectadas a las 9 semanas (61% contra 38 % en los hígados, 59% contra 31% de bazos y 84 % contra 57% en intestinos). Entre las muestras recolectadas a las 21-22 semanas de edad, la frecuencia de recuperación de Salmonella Enteritidis fue nuevamente significativamente mayor en aves infectadas a las 15 semanas de edad que en aquellas infectadas a las 9 semanas (16% contra 6% de bazos, 9% contra 1% en ovarios y 26% contra 10% de los intestinos). Estos datos sugieren que las infecciones por Salmonella Enteritidis introducidas en las parvadas durante las últimas etapas de la cría de pollitas tienen un mayor potencial para persistir en la fase inicial de la producción de huevos. [ABSTRACT FROM AUTHOR]

Diagnostic delay for TB infected individuals and the lack of TB vaccines for adults are the main challenges to achieve the goals of WHO by 2050. In order to evaluate the impacts of diagnostic delay and vaccination for adults on prevalence of TB, we propose an age-structured model with latent age and infection age, and we incorporate Mycobacterium TB in the environment and vaccination into the model. Diagnostic delay is indicated by the age of infection before receiving treatment. The threshold dynamics are established in terms of the basic reproduction number R 0 . When R 0 < 1 , the disease-free equilibrium is globally asymptotically stable, which means that TB epidemic will die out; When R 0 = 1 , the disease-free equilibrium is globally attractive; there exists a unique endemic equilibrium and the endemic equilibrium is globally attractive when R 0 > 1 . We estimate that the basic reproduction number R 0 = 0.5320 (95% CI (0.3060, 0.7556)) in Jiangsu Province, which means that TB epidemic will die out. However, we find that the annual number of new TB cases by 2050 is 1,151 (95%CI: (138, 8,014)), which means that it is challenging to achieve the goal of WHO by 2050. To this end, we evaluate the possibility of achieving the goals of WHO if we start vaccinating adults and reduce diagnostic delay in 2025. Our results demonstrate that when the diagnostic delay is reduced from longer than four months to four months, or 20% adults are vaccinated, the goal of WHO in 2050 can be achieved, and 73,137 (95%CI: (23,906, 234,086)) and 54,828 (95%CI: (15,811, 206,468)) individuals will be prevented from being infected from 2025 to 2050, respectively. The modeling approaches and simulation results used in this work can help policymakers design control measures to reduce the prevalence of TB. [ABSTRACT FROM AUTHOR]

Direct-acting antiviral agents (DAAs) have shown higher cure rates for treating hepatitis C virus (HCV) by directly interfering with different steps of the HCV life cycle. To optimize drug combinations and accurately quantify the antiviral effect of DAAs treatments, mathematical models should include the intracellular virus replication processes. In this study, we develop a two-strain multiscale age-structured model that includes intracellular viral RNA replication and extracellular viral infection. We prove the existence, positivity, and boundedness of the solution, and derive the conditions for the existence and stability of the three steady states (non-infection steady state, boundary steady state, and coexistence steady state). Under certain biologically reasonable assumptions, we obtain the approximate solutions of the viral load decline of the two virus strains (sensitive and drug-resistant virus strains) during treatment, and the long-term approximation is shown to be in good agreement with the solution of the original model. We also carry out numerical simulations using the long-term approximate solution, providing insights into the influence of antiviral effects on the viral load change of the two virus strains during treatment with DAAs. • A multiscale mixed-ODE-PDE model is developed to study HCV infection. • The model includes intracellular RNA replication and extracellular viral infection. • We studied the existence and stability of the three steady states. • The approximate analytical solution is convenient for data comparison. [ABSTRACT FROM AUTHOR]

Hosts can activate a defensive response to clear the parasite once being infected. To explore how host survival and fecundity are affected by host-parasite coevolution for chronic parasitic diseases, in this paper, we proposed an age-structured epidemic model with infection age, in which the parasite transmission rate and parasite-induced mortality rate are structured by the infection age. By use of critical function analysis method, we obtained the existence of the host immune evolutionary singular strategy which is a continuous singular strategy (CSS). Assume that parasite-induced mortality begins at infection age τ and is constant v thereafter. We got that the value of the CSS, c ∗ , monotonically decreases with respect to infection age τ (see Case (I)), while it is non-monotone if the constant v positively depends on the immune trait c (see Case (II)). This non-monotonicity is verified by numerical simulations and implies that the direction of immune evolution depends on the initial value of immune trait. Besides that, we adopted two special forms of the parasite transmission rate to study the parasite’s virulence evolution, by maximizing the basic reproduction ratio R 0 . The values of the convergence stable parasite’s virulence evolutionary singular strategies v ∗ and k ∗ increase monotonically with respect to time lag L (i.e., the time lag between the onset of transmission and mortality). At the singular strategy v ∗ and k ∗ , we further obtained the expressions of the case mortalities χ ∗ and how they are affected by the time lag L. Finally, we only presented some preliminary results about host and parasite coevolution dynamics, including a general condition under which the coevolutionary singular strategy (c ∗ , v ∗) is evolutionarily stable. [ABSTRACT FROM AUTHOR]

Abstract Background Accurate estimation of the burden of Plasmodium falciparum is essential for strategic planning for control and elimination. Due in part to the extreme heterogeneity in malaria exposure, immunity, other causes of disease, direct measurements of fever and disease attributable to malaria can be difficult. This can make a comparison of epidemiological metrics both within and between populations hard to interpret. An essential part of untangling this is an understanding of the complex time-course of malaria infections. Methods Historic data from malariatherapy infections, in which individuals were intentionally infected with malaria parasites, were reexamined in aggregate. In this analysis, the age of each infection was examined as a potential predictor describing aggregate patterns across all infections. A series of piecewise linear and generalized linear regressions were performed to highlight the infection age-dependent patterns in both parasitaemia and gametocytaemia, and from parasitaemia and gametocytaemia to fever and transmission probabilities, respectively. Results The observed duration of untreated patent infection was 130 days. As infections progressed, the fraction of infections subpatent by microscopy was seen to increase steadily. The time-averaged malaria infections had three distinct phases in parasitaemia: a growth phase for the first 6 days of patency, a rapid decline from day 6 to day 18, and a slowly declining chronic phase for the remaining duration of the infection. During the growth phase, parasite densities increased sharply to a peak. Densities sharply decline for a short period of time after the peak. During the chronic phase, infections declined steadily as infections age. gametocytaemia was strongly correlated with lagged asexual parasitaemia. Fever rates and transmission efficiency were strongly correlated with parasitaemia and gametocytaemia. The comparison between raw data and prediction from the age of infection has good qualitative agreement across all quantities of interest for predicting averaged effects. Conclusion The age of infection was established as a potentially useful covariate for malaria epidemiology. Infection age can be estimated given a history of exposure, and accounting for exposure history may potentially provide a new way to estimate malaria-attributable fever rates, transmission efficiency, and patent fraction in immunologically naïve individuals such as children and people in low-transmission regions. These data were collected from American adults with neurosyphilis, so there are reasons to be cautious about extending the quantitative results reported here to general populations in malaria-endemic regions. Understanding how immune responses modify these statistical relationships given past exposure is key for being able to apply these results more broadly.

In this paper, we focus on the global dynamics of a multiscale hepatitis C virus model. The model takes into account the evolution of the virus in cells and RNA. For the model, we establish the globally asymptotical stability of both infection-free and infected equilibria. We first give the basic reproduction number R 0 of the model, and then find that the system holds infected equilibrium when R 0 > 1 . Using eigenvalue analysis, Lyapunov functional, persistence theory and so on, it is proved that infection-free and infected equilibria are globally asymptotically stable when R 0 < 1 and R 0 > 1 , respectively. Thus, extinction and persistence of viruses in cells are theoretically judged. Finally, we show our theoretical results by means of numerical simulation. [ABSTRACT FROM AUTHOR]

In order to treat the diseases caused by hepatitis C virus (HCV) more efficiently, the concentration of HCV in blood, cells, tissues and the body has attracted widespread attention from related scholars. This paper studies a dynamic dependent HCV model (more specifically, including age structure and treatment methods model) that concludes states of infection-free and infected equilibrium. Through eigenvalue analysis and Volterra integral formula, it proves that $ E_0 $ is globally asymptotically stable when $ \mathcal{R} < 1 $. After explaining the existence, uniqueness and positive properties of the solution of the system, we have proved the global asymptotic stability of $ E^* $ when $ \mathcal{R} > 1 $ by constructing a suitable Lyapunov function. Through the above proofs, it can be concluded that effective treatment measures can significantly reduce the number of HCVs, so many related researchers are aware of the importance of highly efficient nursing methods and are committed to applying relevant methods to practice.

Background: Accurate estimation of the burden of Plasmodium falciparum is essential for strategic planning for control and elimination. Due in part to the extreme heterogeneity in malaria exposure, immunity, other causes of disease, direct measurements of fever and disease attributable to malaria can be difficult. This can make a comparison of epidemiological metrics both within and between populations hard to interpret. An essential part of untangling this is an understanding of the complex time-course of malaria infections. Methods: Historic data from malariatherapy infections, in which individuals were intentionally infected with malaria parasites, were reexamined in aggregate. In this analysis, the age of each infection was examined as a potential predictor describing aggregate patterns across all infections. A series of piecewise linear and generalized linear regressions were performed to highlight the infection age-dependent patterns in both parasitaemia and gametocytaemia, and from parasitaemia and gametocytaemia to fever and transmission probabilities, respectively. Results: The observed duration of untreated patent infection was 130 days. As infections progressed, the fraction of infections subpatent by microscopy was seen to increase steadily. The time-averaged malaria infections had three distinct phases in parasitaemia: a growth phase for the first 6 days of patency, a rapid decline from day 6 to day 18, and a slowly declining chronic phase for the remaining duration of the infection. During the growth phase, parasite densities increased sharply to a peak. Densities sharply decline for a short period of time after the peak. During the chronic phase, infections declined steadily as infections age. gametocytaemia was strongly correlated with lagged asexual parasitaemia. Fever rates and transmission efficiency were strongly correlated with parasitaemia and gametocytaemia. The comparison between raw data and prediction from the age of infection has good qualitative agreement across all quantities of interest for predicting averaged effects. Conclusion: The age of infection was established as a potentially useful covariate for malaria epidemiology. Infection age can be estimated given a history of exposure, and accounting for exposure history may potentially provide a new way to estimate malaria-attributable fever rates, transmission efficiency, and patent fraction in immunologically naïve individuals such as children and people in low-transmission regions. These data were collected from American adults with neurosyphilis, so there are reasons to be cautious about extending the quantitative results reported here to general populations in malaria-endemic regions. Understanding how immune responses modify these statistical relationships given past exposure is key for being able to apply these results more broadly. [ABSTRACT FROM AUTHOR]

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 multi-group 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 R0 has been computed. The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R0. More precisely, for R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable and for R0 > 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. [ABSTRACT FROM AUTHOR]

In this paper, an SIQR-Epidemic transmission model of the non-Markovian infection process and quarantine process in a heterogeneous complex network is established, in which the infection rate and quarantine rate are related to infection age. Next, we use the method of characteristics to transform the model into an integro-differential equation and derive the epidemic threshold of the model. Finally, we focus on the impact of three different infection or quarantine time distributions on the disease transmission and show that infection or quarantine time distribution has a significant effect on the disease dynamics. [ABSTRACT FROM AUTHOR]

In this paper, an age-structured HIV-1 infection model with CTL immune response is investigated. In the model, we consider the infection age (i.e. the time that has elapsed since an HIV virion has penetrated the cell) of infected $T$ cells. The asymptotic smoothness of the semi-flow generated by the system is established. By calculation, the immune-inactivated reproduction rate $\mathscr{R}_0$ and the immune-activated reproduction rate $\mathscr{R}_1$ are obtained. By analyzing the corresponding characteristic equations, the local stability of an infection-free steady state and a CTL-inactivated infection steady state of the model is established. By using the persistence theory for infinite dimensional system, the uniform persistence of the system is established when $\mathscr{R}_1>1$. By means of suitable Lyapunov functionals and LaSalle's invariance principle, it is shown that if $\mathscr{R}_0 < 1$, the infection-free steady state is globally asymptotically stable; if $\mathscr{R}_1 < 1 < \mathscr{R}_0$, sufficient conditions are derived for the global stability of the CTL-inactivated infection steady state; if $\mathscr{R}_1>1$, sufficient conditions are obtained for the global attractivity of the CTL-activated infection steady state. Numerical simulations are carried out to illustrate the feasibility of the theoretical results.

In this paper, we focus on the study of the dynamics of a certain age structured epidemic model. Our aim is to investigate the proposed model, which is based on the classical SIR epidemic model, with a general class of nonlinear incidence rate with some other generalization. We are interested to the asymptotic behavior of the system. For this, we have introduced the basic reproduction number ${\cal R}_0$ of model and we prove that this threshold shows completely the stability of each steady state. Our approach is the use of general constructed Lyapunov functional with some results on the persistence theory. The conclusion is that the system has a trivial disease-free equilibrium which is globally asymptotically stable for ${\cal R}_0 \lt 1$ and that the system has only a unique positive endemic equilibrium which is globally asymptotically stable whenever ${\cal R}_0 \gt 1$. Several numerical simulations are given to illustrate our results.

In this article, we propose an infection age-structured multi-strain SIS epidemic model on complex networks. We obtain the reproduction numbers for each strain by using the classical theory of renewal equations, and we define the basic reproduction number $\mathcal{R}_0$ for the whole system by the maximum of them. We prove that if $\mathcal{R}_0 < 1$, then the disease-free equilibrium of the model is globally asymptotically stable, whereas if $\mathcal{R}_0 > 1$, then there exists an endemic equilibrium in which only one strain with the largest reproduction number survives. Moreover, under an additional assumption that the recovery rate is homogeneous, we prove that such an endemic equilibrium is globally asymptotically stable. Interestingly, our theoretical results imply that the competitive exclusion can occur in a sense that only one strain with the largest reproduction number survives.

This paper studies a two-strain SIS pairwise approximation model with a competing mechanism and non-Markovian recovery process in which the recovery rate depends on infection age. The model is a hyperbolic system, which can be transformed into a system of integro-differential equations by using the method of characteristics. We obtain the associated reproduction numbers for each of the two strains, which determine the existence of the boundary equilibria. Besides, we also show that the two competing strains may coexist.

The demography and infection age play an important role in the spread of slowly progressive diseases. To investigate their effects on the disease spreading, we propose a pairwise epidemic model with infection age and demography on dynamic networks. The basic reproduction number of this model is derived. It is proved that there is a disease-free equilibrium which is globally asymptotically stable if the basic reproduction number is less that unity. Besides, sensitivity analysis is performed and shows that increasing the variance in recovery time and decreasing the variance in infection time can effectively control the diseases. The complex interaction between the death rate and equilibrium prevalence suggests that it is imperative to correctly estimate the parameters of demography in order to assess the disease transmission dynamics accurately. Moreover, numerical simulations show that the endemic equilibrium is globally asymptotically stable.

Abstract In this paper, we propose a within-host HIV-1 epidemic model with cell-to-virus and cell-to-cell transmission. By mathematical analysis, we obtain the basic reproduction number R 0 $\mathcal {R}_{0}$ , which determines the viral persistence and the basic reproduction number R 0 cc $\mathcal {R}_{0}^{\mathrm{cc}}$ with respect to cell-to-cell transmission which is not strong enough, i.e., it is less than 1. If the basic reproduction number is less than 1, then the viral-free steady state E 0 $E_{0}$ is globally asymptotically stable, which is proved by fluctuation lemma and comparison method; if R 0 > 1 $\mathcal {R}_{0}>1$ is greater than 1, the endemic steady state E ∗ $E^{*}$ is globally asymptotically stable, which is proved by constructing the Lyapunov functional. Antiretoviral therapy is implemented to suppress the viral replication. Protease inhibitors for cell-to-cell transmission play an important role in controlling cell-to-cell infection. Under some circumstances, the effects of the cell-to-cell infection process are more sensitive than those of cell-to-virus transmission.

In this paper, we propose an SIVS epidemic model with continuous age structures in both infected and vaccinated classes and with a general nonlinear incidence. Firstly, we provide some basic properties of the system including the existence, uniqueness and positivity of solutions. Furthermore, we show that the solution semiflow is asymptotic smooth. Secondly, we calculate the basic reproduction number $ \mathcal {R}_0 $ by employing the classical renewal process, which determines whether the disease persists or not. In the main part, we investigate the global stability of the equilibria by the approach of Lyanpunov functionals. Some numerical simulations are conducted to illustrate the theoretical results and to show the effect of the transmission rate and immunity waning rate on the disease prevalence.

This paper is devoted to studying the dynamics of a certain age structured heroin-cocaine epidemic model. More precisely, this model takes into account the following unknown variables: susceptible individuals, heroin users, cocaine users and recovered individuals. Each one of these classes can change or interact with others. In this paper, firstly, we give some results on the existence, uniqueness and positivity of solutions. Next, we obtain a threshold value r(Ψ′ [0]) such that an endemic equilibrium exists if r(Ψ′ [0]) > 1. We then show that if r(Ψ′ [0]) < 1, then the disease-free equilibrium is globally asymptotically stable, whereas if r(Ψ′ [0]) > 1, then the system is uniformly persistent. Moreover, for r(Ψ′ [0]) > 1, we show that the endemic equilibrium is globally asymptotically stable under an additional assumption that epidemic parameters for heroin users and cocaine users are same. Finally, some numerical simulations are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the global asymptotic behavior of an infection age-structured SIR epidemic model with diffusion in a general n -dimensional bounded spatial domain under the homogeneous Dirichlet boundary condition. By using the method of characteristics, we reformulate the model into a system of a reaction-diffusion equation and a Volterra integral equation. We define the basic reproduction number R 0 by the spectral radius of a compact positive linear operator and show that if R 0 < 1 , then the disease-free steady state is globally attractive, whereas if R 0 > 1 , then a positive endemic steady state exists and the system is uniformly persistent. By numerical simulation for the 2-dimensional case, we show that R 0 depends on the shape of the spatial domain. This result is in contrast with the case of the homogeneous Neumann boundary condition, in which R 0 is independent of the spatial domain. [ABSTRACT FROM AUTHOR]

We propose and analyse an age-structured model for within-host HIV virus dynamics which is incorporated with both virus-to-cell and cell-to-cell infection routes, and proliferations of both uninfected and infected cells in the form of logistic growth. The model turns out to be a hybrid system with two differential-integral equations and one first-order partial differential equation. We perform some rigorous analyses for the considered model. Among the interesting dynamical behaviours of the model is the occurrence of backward bifurcation in terms of the basic reproduction number R0 at R0 = 1, which raises new challenges for effective infection control. We also discuss the cause of such a backward bifurcation, based on our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with an SIR epidemic model with infection age and spatial diffusion in the case of Neumann boundary condition. The original model is constructed as a nonlinear age structured system of reaction–diffusion equations. By using the method of characteristics, we reformulate the model into a system of a reaction–diffusion equation and a Volterra integral equation. For the reformulated system, we define the basic reproduction number R 0 by the spectral radius of the next generation operator, and show that if R 0 < 1 , then the trivial disease-free steady state is globally attractive, whereas if R 0 > 1 , then the disease in the system is persistent. Moreover, under an additional assumption that there exists a finite maximum age of infectiousness, we show the global attractivity of a constant endemic steady state for R 0 > 1. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a general class of SIRISIRI age infection structured model where infectivity depends on the age since infection and where some individuals from the RR class, also called quarantaine class in this work, can return to the infectiousness class after a while. Using classical technics we compute a basic reproductive number R0R0 and show that the disease dies out when R0<1R0<1 and persists if R0>1R0>1. Some Lyapunov suitable functions are derived to prove global stability for the disease free equilibrium (DFE) when R0<1R0<1 and for the endemic equilibrium (EE) when R0>1R0>1. Using numerical results we show that the non homogeneous infectivity combined with the feedback to the infectiousness class of a part of the quarantaine population modifies drastically the behavior of the epidemic. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of a SEIR (susceptible-exposed-infectious-recovered) model with the age of infection and vaccination. Firstly, we prove the positivity, boundedness, and asymptotic smoothness of the solutions. Next, the existence and local stability of disease-free and endemic steady states are shown. The basic reproduction number R0 is introduced. Furthermore, the global stability of the disease-free and endemic steady states is derived. Numerical simulations are shown to illustrate our theoretical results.

A susceptible-vaccinated-infectious-recovered epidemic model with infection age and relapse age has been formulated. We first address the asymptotic smoothness of the solution semiflow, existence of a global attractor, and uniform persistence of the model. Then by constructing suitable Volterra-type Lyapunov functionals, we establish a global threshold dynamics of the model, which is determined by the basic reproduction number. Biologically, it is confirmed that neglecting the possibility of vaccinees getting infected will over-estimate the effect of vaccination strategies. The obtained results generalize some existing ones.

• A two-strain pairwise epidemic model with non-Markovian recovery process is established. • A hyperbolic system can be transformed into an integral differential system by using the method of characteristic. • We carry out rigorous analysis and obtain the relationship between the reproduction number and the final epidemic size. • Three commonly used recovery time distributions on the reproduction number were compared by numerical simulations. • The mean length of the infectious period affects the final epidemic size, the peak time, and the duration of an epidemic. We present and study a two-strain pairwise epidemic model with non-Markovian recovery process in which the recovery rate depends on infection age. The novel model is a hyperbolic system which can be transformed into a system of integro-differential equations by using the method of characteristics. For the two-strain pairwise model, the reproduction number with arbitrary recovery time distributions is obtained. We carry out rigorous analysis and obtain upper and lower estimates for the final epidemic size. Finally, the effects of three commonly used recovery time distributions on the reproduction number are compared by numerical simulations. We further present how the mean length of the infectious period affects the final epidemic size, the peak time and the duration of an epidemic. [ABSTRACT FROM AUTHOR]

In this paper, we propose an SIVS epidemic model with continuous age structures in both infected and vaccinated classes and with a general nonlinear incidence. Firstly, we provide some basic properties of the system including the existence, uniqueness and positivity of solutions. Furthermore, we show that the solution semiflow is asymptotic smooth. Secondly, we calculate the basic reproduction number by employing the classical renewal process, which determines whether the disease persists or not. In the main part, we investigate the global stability of the equilibria by the approach of Lyanpunov functionals. Some numerical simulations are conducted to illustrate the theoretical results and to show the effect of the transmission rate and immunity waning rate on the disease prevalence. [ABSTRACT FROM AUTHOR]

The demography and infection age play an important role in the spread of slowly progressive diseases. To investigate their effects on the disease spreading, we propose a pairwise epidemic model with infection age and demography on dynamic networks. The basic reproduction number of this model is derived. It is proved that there is a disease-free equilibrium which is globally asymptotically stable if the basic reproduction number is less that unity. Besides, sensitivity analysis is performed and shows that increasing the variance in recovery time and decreasing the variance in infection time can effectively control the diseases. The complex interaction between the death rate and equilibrium prevalence suggests that it is imperative to correctly estimate the parameters of demography in order to assess the disease transmission dynamics accurately. Moreover, numerical simulations show that the endemic equilibrium is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

In this paper, an age-structured cholera model with both human-to-human and environment-to-human transmissions and saturation incidence is proposed. In the model, we consider the infection age of infectious individuals and the biological age of pathogen in the environment. It is verified that the global dynamics of the model is completely determined by the basic reproduction number. Asymptotic smoothness is verified as a necessary argument. By analyzing corresponding characteristic equations, we discuss the local stability of each of feasible steady states. Uniform persistence is shown by using the persistence theory for infinite dimensional dynamical system. The global stability of each of feasible steady states is established by using suitable Lyapunov functionals and LaSalle’s invariance principle. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

A vector-borne disease model with general incidence rates is proposed and investigated in this paper, where both vector and host are stratified by infection ages in the form of a hyperbolic system of partial differential equations coupled with ordinary differential equations. The existence, uniqueness, nonnegativeness, and boundedness of solution of the model are studied for biologically reasonable purpose. Furthermore, a global threshold dynamics of the system is established by constructing suitable Lyapunov functionals, which is determined by the basic reproduction number R0: the infection-free equilibrium is globally asymptotically stable when R0<1 while the endemic equilibrium is globally asymptotically stable when R0>1. [ABSTRACT FROM AUTHOR]

Infection age is often an important factor in epidemic dynamics. In order to realistically analyze the spreading mechanism and dynamical behavior of epidemic diseases, in this paper, a generalized disease transmission model of SIS type with age-dependent infection and birth and death on a heterogeneous network is discussed. The model allows the infection and recovery rates to vary and depend on the age of infection, the time since an individual becomes infected. We address uniform persistence and find that the model has the sharp threshold property, that is, for the basic reproduction number less than one, the disease-free equilibrium is globally asymptotically stable, while for the basic reproduction number is above one, a Lyapunov functional is used to show that the endemic equilibrium is globally stable. Finally, some numerical simulations are carried out to illustrate and complement the main results. The disease dynamics rely not only on the network structure, but also on an age-dependent factor (for some key functions concerned in the model). [ABSTRACT FROM AUTHOR]

For epidemic models, it is shown that fatal infectious diseases cannot drive the host population into extinction if the incidence function is upper density-dependent. This finding holds even if a latency period is included and the time from infection to disease-induced death has an arbitrary length distribution. However, if the incidence function is also lower density-dependent, very infectious diseases can lead to a drastic decline of the host population. Further, the final population size after an epidemic outbreak can possibly be substantially affected by the infection-age distribution of the initial infectives if the life expectations of infected individuals are an unbounded function of infection age (time since infection). This is the case for lognormal distributions, which fit data from infection experiments involving tiger salamander larvae and ranavirus better than gamma distributions and Weibull distributions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a within-host HIV-1 epidemic model with cell-to-virus and cell-to-cell transmission. By mathematical analysis, we obtain the basic reproduction number $\mathcal {R}_{0}$ , which determines the viral persistence and the basic reproduction number $\mathcal {R}_{0}^{\mathrm{cc}}$ with respect to cell-to-cell transmission which is not strong enough, i.e., it is less than 1. If the basic reproduction number is less than 1, then the viral-free steady state $E_{0}$ is globally asymptotically stable, which is proved by fluctuation lemma and comparison method; if $\mathcal {R}_{0}>1$ is greater than 1, the endemic steady state $E^{*}$ is globally asymptotically stable, which is proved by constructing the Lyapunov functional. Antiretoviral therapy is implemented to suppress the viral replication. Protease inhibitors for cell-to-cell transmission play an important role in controlling cell-to-cell infection. Under some circumstances, the effects of the cell-to-cell infection process are more sensitive than those of cell-to-virus transmission. [ABSTRACT FROM AUTHOR]

In this paper, an SVIR epidemiological model with infection age (time elapsed since the infection) and nonlinear incidence is studied. In the model, in order to reflect the dependence of disease progress on the infection age, the infected individual is structured by the infection age, and transmission and removal rates are assumed to depend on the infection age. By analyzing corresponding characteristic equations, the local stability of each of steady states of the model is established. It is proved that the semi-flow generated by this system is asymptotically smooth, and if the basic reproduction number is greater than unity, the system is uniformly persistent. By using Lyapunov functional and LaSalle's invariance principle, the global dynamics of the model is investigated. It is shown that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable and hence the disease dies out; and if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable and the disease persists. Numerical simulations are carried out to illustrate the main analytic results. [ABSTRACT FROM AUTHOR]

For the long term population behavior, demography is a very important factor impacting the disease spread. Infection age also helps us better understand the process of the disease transmission. In this paper, we incorporate these two factors in an SIR epidemic model on complex networks. Through mathematical analysis, the basic reproduction number R 0 is shown to be a sharp threshold to determine whether or not the disease spreads. Precisely, if R 0 is less than 1 then the disease-free equilibrium is globally asymptotically stable while if R 0 is larger than 1 then the endemic equilibrium is globally asymptotically stable. Some simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

A susceptible-vaccinated-infectious-recovered epidemic model with infection age and relapse age has been formulated. We first address the asymptotic smoothness of the solution semiflow, existence of a global attractor, and uniform persistence of the model. Then by constructing suitable Volterra-type Lyapunov functionals, we establish a global threshold dynamics of the model, which is determined by the basic reproduction number. Biologically, it is confirmed that neglecting the possibility of vaccinees getting infected will over-estimate the effect of vaccination strategies. The obtained results generalize some existing ones. [ABSTRACT FROM PUBLISHER]

To understand the current quality status and rearing situation of Bombyx Batryticatus, the authors collected 102 batches of Bombyx Batryticatus from different main producing areas and five major Chinese medicine markets from 2016 to 2018, and measured the properties and quality of the silk gland, to clarify the quality status of Bombyx Batryticatus from different producing areas and markets. In addition, 35 batches of Bombyx Batryticatus from 2019 to 2022 were used to verify the silk gland after revision. Moreover, Beauveria Bassiana was inoculated in the silkworm of 4-5 instars, and standardized rearing was carried out until they die. The death rate and the quality of Bombyx Batryticatus were measured to determine the differences in Bombyx Batryticatus of different instars, and explore the rationality of the infection age of Bombyx Batryticatus in Chinese Pharmacopoeia(2020). The results revealed that in the 102 batches of Bombyx Batryticatus, the qualification rate of silk gland was low; the content of total ash far exceeded the standard; the content of beauvericin varied greatly. The qualification rate of the silk gland of the 35 batches of Bombyx Batryticatus was only 47.49%, which could be increased to 73.00% if the number of silk gland was 2 to 4. The death rate of Bombyx Batryticatus at different infection ages was quite different, with uneven quality. Generally, the yield of Bombyx Batryticatus inoculated on the first day of the fifth instar was high with good quality. Therefore, in combination with the quality and actual production of Bombyx Batryticatus, the following suggestions were proposed for revision of Bombyx Batryticatus in Chinese Pharmacopoeia(2025): The number of silk gland should be revised as 2-4 bright brown or bright black silk glands, after which, the quality of Bombyx Batryticatus could be guaranteed, and the &quot;quality identification based on character&quot; could also be reflected scientifically; the content determination index that the content of beauvericin shall not be less than 0.017% should be added to better control the quality of Bombyx Batryticatus; the infection age should be revised as the first day of the fifth instar to narrow the age span, which could better fit the actual production and ensure the quality of Bombyx Batryticatus.

In this paper, based on an SIS model, we construct an epidemic model with infection age to investigate the disease transmission on complex networks. By analyzing the characteristic equations associated with the equilibria, we obtain the basic reproduction number $$R_0$$ . It is shown that if $$R_0<1$$ then the disease-free equilibrium is globally asymptotically stable while if $$R_0>1$$ then there is a unique endemic equilibrium, which is asymptotically stable. Our investigation indicates that if the maximal degree of the network is large enough then the endemic equilibrium always exists. Sensitivity analysis on the basic reproduction number $$R_0$$ in terms of the parameters is carried out to illustrate their effects on the disease transmission and to develop appropriate control strategies. [ABSTRACT FROM AUTHOR]

Although many studies have proposed different multi-group epidemic models, few models considering that the vaccinated class may lose their protective properties at different rates have been developed. In this paper, we formulate a new multi-group SVEIR epidemic model that incorporates both the vaccination age of vaccinated individuals and the infection age of infectious individuals. We show that the basic reproduction number $R_{0}$ plays an important role in determining the long-term dynamics, that is, if $R_{0}\leq1$, then the disease-free equilibrium is globally asymptotically stable while if $R_{0}>1$, an endemic equilibrium uniquely exists and is globally asymptotically stable by using a graph-theoretic approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is shown to be helpful for disease control by decreasing the basic reproduction number, either enhancing the vaccination rate or lengthening the duration of vaccination protection. [ABSTRACT FROM AUTHOR]

Epidemic models with infection age have been extensively studied in the recent decades. Unfortunately, the incidence rate used is the bilinear one. As incidence rate plays an important role in disease transmission, in this paper, we study an SIR epidemic model with infection age and saturated incidence. We establish a threshold dynamics by applying the fluctuation lemma and Lyapunov functional. Roughly, if the basic reproduction number is less than 1 , then the disease-free equilibrium is globally asymptotically stable; while if the basic reproduction number is larger than 1 , then the endemic equilibrium is globally asymptotically stable in the set with initial infectivity. [ABSTRACT FROM AUTHOR]