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In this paper, we study an age-structured population model with non-local diffusion and distributed delay. By using the non-densely defined operators and extended phase spaces, we first rewrite the model into an abstract ordinary differential equation. Then we prove the existence of the solution of the model by using the operator semigroup theory. Finally, we study the spectrum of the non-densely defined operators and analyze the asymptotic behavior via asynchronous exponential growth. Our results extend the results for the age-structured population models without time delay. [ABSTRACT FROM AUTHOR]

Abstract Objective To assess the impact of self-medication on the transmission dynamics of COVID-19 across different age groups, examine the interplay of vaccination and self-medication in disease spread, and identify the age group most prone to self-medication. Methods We developed an age-structured compartmentalized epidemiological model to track the early dynamics of COVID-19. Age-structured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters. Results We found that self-medication is predominant among the age group 15-64 (74.52%), followed by the age group 0-14 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that self-medication among individuals aged 15-64 results in the highest spreading rate of COVID-19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing. Conclusion Studies aiming to understand the dynamics of diseases in areas prone to self-medication should account for this practice. There is a need for a campaign against COVID-19-related self-medication, specifically targeting the active population (ages 15-64).

Objective: To assess the impact of self-medication on the transmission dynamics of COVID-19 across different age groups, examine the interplay of vaccination and self-medication in disease spread, and identify the age group most prone to self-medication. Methods: We developed an age-structured compartmentalized epidemiological model to track the early dynamics of COVID-19. Age-structured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters. Results: We found that self-medication is predominant among the age group 15-64 (74.52%), followed by the age group 0-14 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that self-medication among individuals aged 15-64 results in the highest spreading rate of COVID-19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing. Conclusion: Studies aiming to understand the dynamics of diseases in areas prone to self-medication should account for this practice. There is a need for a campaign against COVID-19-related self-medication, specifically targeting the active population (ages 15-64). [ABSTRACT FROM AUTHOR]

Recent studies reveal that pyroptosis is associated with the release of inflammatory cytokines which can attract more target cells to be infected. In this paper, a novel age-structured virus infection model incorporating cytokine-enhanced infection is investigated. The asymptotic smoothness of the semiflow is studied. With the help of characteristic equations and Lyapunov functionals, we have proved that both the local and global stabilities of the equilibria are completely determined by the threshold $ \mathcal{R}_0 $. The result shows that cytokine-enhanced viral infection also contributes to the basic reproduction number $ \mathcal{R}_0 $, implying that it may not be enough to eliminate the infection by decreasing the basic reproduction number of the model without considering the cytokine-enhanced viral infection mode. Numerical simulations are carried out to illustrate the theoretical results.

This paper is concerned with a class of age-structured cholera model with general infection rates. We first explore the existence and uniqueness, dissipativeness and persistence of the solutions, and the existence of the global attractor by verifying the asymptotical smoothness of the orbits. We then give mathematical analysis on the existence and local stability of the positive equilibrium. Based on the preparation, we further investigate the global behavior of the cholera infection model. Corresponding numerical simulations have been presented. Our results improve and generalize some known results on cholera models.

The spread and control of infectious diseases are inevitably influenced by the age structure of the population and media effect. In this paper, we propose a susceptible-exposure-infection-recovery type age-structured COVID-19 model with media effect. First, the existence and uniqueness of the solution are obtained using semigroup theory and the positive operator method. The basic regeneration number R 0 is computed next and the globally asymptotical stability of the disease-free steady state, as well as the locally asymptotical stability of endemic steady state is studied without any extra conditions. The influence of media effect and age structure of the population on disease transmission are also verified by numerical simulations. Our result show that additional intensity of media broadcasts not only reduces the peak of disease outbreak but also shortens the duration of the epidemic. Further more, the proportion of infected adolescents is lower, and adults should pay more attention to self-protection. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the impact of the varying population sizes on the dynamic behavior of the age-structured epidemic model. A age-structured SIRS epidemic model with the varying population sizes is established and investigated to take into account time delay. The non-negativity of the solution, the existence and stability of the steady states, and the existence of the Hopf bifurcation are discussed. The numerical simulations show that the varying population sizes can cause the age-structured SIRS model to produce multiple stability switches.

This paper establishes an age-structured Tuberculosis (TB) model to investigate the joint impacts of information and immigration of population on the spread of TB disease. Mathematically, we show that the model is point dissipative, and the semi-flow generated by the model has the property of asymptotic smoothness, and then study the existence and global stability of positive steady state by the direct Lyapunov functional. Numerically, by using Matlab software, we verify the theoretical results, and further explore the influence of information (including information coverage and disease-related memory delay) and immigration on the final size of TB disease. The simulation results show that both information coverage and immigration are positive correlated with the final size of disease, and disease-related memory delay can affect the arrival time of positive steady state, which implies us that improving information coverage, enlarging disease-related memory, and reducing the immigration of population (especially latent and infected individuals) can effectively control the progression of TB disease. [ABSTRACT FROM AUTHOR]

In this paper, we study an age‐structured reaction‐diffusion‐advection population model. First, we use a non‐densely defined operator to the linear age‐structured reaction‐diffusion‐advection population model in a patchy environment. By spectral analysis, we obtain the asynchronous exponential growth of the population model. Then we consider nonlinear death rate and birth rate, which all depend on the function related to the generalized total population, and we prove the existence of a steady state of the system. Finally, we study the age‐structured reaction‐diffusion‐advection population model in non‐autonomous situations. We give the comparison principle and prove the eventual compactness of semiflow by using integrated semigroup. We also prove the existence of compact attractors under the periodic situation. [ABSTRACT FROM AUTHOR]

The housefly is a dominant species in most places and is widely distributed worldwide. However, it is becoming more troublesome that they are not only closely related to human life but can also seriously endanger human health and spread many diseases. Thus, in this paper, a more exhaustive dynamical explanation involving houseflies' DDE and reduced ODE models is elucidated by employing graphical methods, in which these conclusions are the essence of the predecessors. Hereafter, the houseflies model is considered as a houseflies-age-structured model with a biologically more realistic fertility function by using the theory of integrated semigroups, after which this model is transformed as a non-densely defined Cauchy problem. We also investigate model's equilibria and linearized equation, including the characteristic equation about equilibria and the local stability of the boundary equilibrium. Then, the geometric stability switch criteria are used to examine the Hopf bifurcation of the positive equilibrium, whose characteristic equation coefficients depend on the bifurcation parameter. Additionally, numerical simulations enrich the effectiveness of our model. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the impact of the varying population sizes on the dynamic behavior of the age-structured epidemic model. A age-structured SIRS epidemic model with the varying population sizes is established and investigated to take into account time delay. The non-negativity of the solution, the existence and stability of the steady states, and the existence of the Hopf bifurcation are discussed. The numerical simulations show that the varying population sizes can cause the age-structured SIRS model to produce multiple stability switches. [ABSTRACT FROM AUTHOR]

We consider an age-structured bioeconomic model of a fishery where periodic negative shocks affect recruitment and somatic growth. The model is relevant for fish stocks that are subject to environmentally driven events such as diseases, match-mismatch relationships between plankton blooms and spawning, or recruitment failure. The nature of the optimal fishing strategy is pulse fishing. We vary the period and severity of the shocks to investigate how the optimal management scheme adapts and what factors trigger fishing pulses. Two principles largely govern fishing. The first is to harvest when the number of small cohorts in the stock is minimal. Small cohorts emerge from negative shocks to recruitment. The second principle is to fish when shocks to growth have the least impact on the weight distribution in the stock. Furthermore, we consider how net present value and total catches depend on the period of shocks and the average impact (impact times frequency). In the case of average impacts, we observe close to linear relationships that make reasonable generalizations of our results, for example to different impact levels, viable. The structure of predictable negative shocks in the model is a significant simplification but allows us to crystallize drivers of adaptations in the fishing strategy. [ABSTRACT FROM AUTHOR]

Considering that the creation of marine reserves is one potential solution to the over exploitation of marine life and different population age implies different reproduction as well as survival capacities, we propose an age‐structured predator‐prey model for fishery resource with reserve area where fishing is strictly prohibited, and then consider the corresponding optimal harvesting problem where the objective functional represents the total economic benefits obtained from the harvesting process. First, the existence and uniqueness of the solution of the model are proved by means of the fixed point theorem. Then, the optimality conditions for achieving the optimal harvesting policy are given by solving the extremum point of the cost functional. Furthermore, the existence of a unique optimal harvesting strategy is demonstrated with the use of Ekeland's Principle. Finally, the numerical simulations indicate that the creation of marine reserves is indeed conducive to the recovery of fishery resources, increasing fish abundance and protecting biodiversity as well as ecosystem structure. [ABSTRACT FROM AUTHOR]

In this paper, we studied a two-patch age-structured model of tuberculosis in a context where the migration is not controlled. Motivated by the fact that no author has highlighted the impact of migration on the dynamics of transmission of tuberculosis. Each subpopulation is subdivided into five compartments: susceptible; latent, vaccinated, infective and treated. After the determination of the reproductive numbers ℜ(ψ, ρ) and ℜ0(ρ), we established the conditions of the global and local stability of the equilibrium point without disease. It has been shown that there is only one point of endemic equilibrium. Numerical simulations show that uncontrolled migration negatively influences the dynamics of tuberculosis. [ABSTRACT FROM AUTHOR]

We formulate an age‐structured SEIR epidemic model using vaccination and treatment as control measures. Using the method of characteristics and fixed point arguments, we prove the existence of a unique positive solution to our proposed nonlinear model. We use a suitable objective functional and prove the existence of optimal control variables. Depending on the nature of the problem, the necessary conditions for the optimal control problem are established using the maximum principle of Pontryagin's type. Tools of control theory are used for obtaining optimal control characterizations in terms of state and adjoint variables. To illustrate theoretical results, parameter values are chosen to simulate both with and without control problems. Numerical findings reveal that when, where, and to whom control measures should be implemented for best results of a control program. [ABSTRACT FROM AUTHOR]

An age-structured susceptible–exposed–infected–recovered–susceptible (SEIRS) endemic model is proposed in this analysis utilizing the tools of partial differential equations. Because of different outflows and inflows that are lopsided by migration and demographics factors, the population is supposed to be not constant. To demonstrate that the model is well-posed, an abstract Cauchy problem is developed from the proposed system. The simple reproduction number R 0 is used to analyze the local and global behavior of the disease-free equilibrium. The disease present equilibrium point is shown to exist and be stable locally under appropriate assumptions and conditions. We consider the age-free parameters and the problem is converted into an ordinary differential equations (ODEs) model. The ODEs model is investigated for disease-free and endemic equilibria and the global stability of each equilibrium is presented therein. A few simulations are carried out and discussed at the end of the paper to explain the central theorem of the study. [ABSTRACT FROM AUTHOR]

As the COVID-19 is still spreading in more than 180 countries, according to WHO. There is a need to understand the dynamics of this infection and predict its the impact on the public health capacity. This work aims to forecast the progress of the disease in three countries from different continents: The United States of America, the United Arab Emirates and Algeria. The existing data shows that the fatality of the disease is high in elderly people and people with comorbidity. Therefore, we consider an age-structured model. Our model also takes into consider two main components of the COVID-19 (a) the number of Infected hospitalized people, therefore, we estimate the number of beds (acute and critical) needed (2) the possible infection of the healthcare personals (HCP). Hence, the model predict the peak time and the number of infectious cases at the peak before and after the implementation of non-pharmaceutical interventions (NPI), and we also compare this finding with case of full lockdown. Finally, we investigate the impact of the shortage of proper personal protective equipment (PPE) on the spread of the disease.

Malaria is an infectious vector-borne disease of global public concern, with high morbidity and mortality in children less than 5 years old. We propose a two-group malaria model structured by age with the SEISdynamic in individuals aged below 5 years old, and SEIRSdynamic in individuals aged above 5 years. We compute the basic reproduction number and show that the DFE is locally asymptotically stable when R01, we prove the existence of a unique endemic equilibrium. On the other hand, if R0≤1, under certain conditions, the system can have one endemic equilibrium or two endemic equilibria. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. The average per capita biting rate of mosquitoes on susceptible humans under 5 years old b2, recovery rate of infectious humans under 5 years old ωe, recovery rate of infectious humans over 5 years old ωaand the recruitment of mosquitoes Λvare the most impactful parameters. Graphically, it is shown that any intervention to reduce the contact between the mosquito and individuals under five has a greater positive impact on the level of endemicity in the total population compared to the case when the contact between mosquitoes and individuals over 5 years old is reduced. The public health implication of this result is that the fight against malaria should be stepped up in children under 5 years old to mitigate its spread.

Early vaccination efforts and non-pharmaceutical interventions (NPIs) were insufficient to prevent a surge of COVID-19 cases triggered by the Delta variant. A compartment model that includes age, vaccination, and variants was developed. We estimated the transmission rates using maximum likelihood estimation, and phase-dependent NPIs according to government policies from 26 February to 8 October 2021. Simulations were done to examine the effects of varying dates of initiation and intensity of eased NPIs, arrival timing of Delta, and speed of vaccine administration. The estimated transmission rate matrices show distinct patterns, with transmission rates of younger groups (0-39 years) much larger with Delta. Social distancing (SD) level 2 and SD4 in Korea were associated with transmission reduction factors of 0.63-0.70 and 0.70-0.78, respectively. The easing of NPIs to a level comparable to SD2 should be initiated not earlier than 16 October to keep the number of severe cases below Korea's healthcare capacity. Simulations showed that a surge prompted by Delta can be prevented if the number of people vaccinated daily or SD level when Delta arrived was higher. The timing of easing, intensity of NPIs, vaccination speed, and screening measures are key factors in preventing another epidemic wave. [ABSTRACT FROM AUTHOR]

Human‐induced environmental change is a major stressor on freshwater habitats that has resulted in the population declines of many freshwater species. Ontogenetic shifts in habitat use and associated (st)age‐specific requirements mean that impacts of environmental stressors can influence (st)ages in a population differently, and yet relatively few studies of freshwater fish populations account for their detail.We aimed to identify environmental and biotic factors affecting survival estimated for six age‐classes of a European grayling population in the River Wylye, UK over a 17‐year period. We used a Bayesian age‐structured state space model to estimate survival of grayling cohorts between subsequent life stages (eggs to age 5 adults) for 16 annual transitions (2003–2004 to 2018–2019), whilst accounting for imperfect sampling of the population. We quantified the effects of seasonal water flow and temperature, in‐stream habitat and prey resource, and potential competitors and predators on survival between subsequent life stages. We used Bayesian variable selection to gauge their relative importance on survival.Grayling abundances declined during the study period (>75% in all age‐classes), predominately driven by a loss of mature adults. Changes to seasonal flows negatively influenced their survival: increased days of summer low flow related to decreased survival of subadults and mature adults, and lower winter flows related to reduced recruitment of juveniles from eggs. Higher summer macrophyte cover negatively influenced juvenile and subadult survival and increasing days of high temperature in summer appeared detrimental to juvenile survival. Abundance of brown trout (a potential competitor and predator) did not negatively influence grayling survival.Our results reveal the implications of environmental change on a salmonid population, where recent low summer flows and high temperatures, and below average winter flows, have negatively influenced grayling survival. These conditions appear to be becoming more frequent and persistent in our study river, which is towards the species' southern range limit, which could render the population vulnerable to climate change. Our study demonstrates how careful analysis of long‐term population monitoring and environmental datasets can identify factors affecting (st)age‐specific fish population dynamics, and when combined with local expertise, results in realistic mitigation proposals to promote wildlife population persistence. [ABSTRACT FROM AUTHOR]

In this paper, we formulate an age-structured HIV model, in which the influence of humoral immunity and the infection age of the infected cells are considered. The model is governed by three ordinary differential equations and two first-ordered partial differential equations and admits three equilibria: disease-free, immune-inactivated and immune-activated equilibria. We introduce two important thresholds: the basic reproduction number R 0 and immune-activated reproduction number R 1 and further show the global stability of above three equilibria in terms of R 0 and R 1 , respectively. The numerical simulations are presented to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study stationarity of an age‐structured human immunodeficiency virus (HIV) model with a delay and driven by the Ornstein–Uhlenbeck process. The HIV model involves cell‐to‐virus infection and cell‐to‐cell transmission, and the two transmission modes have a short intracellular latency described by the delay. As the death rate and virus production rate of infected cells have an explicit age‐dependent feature and may be affected by environmental noises, we formulate a stochastic age‐structured HIV model to investigate the impacts of the two transmission modes on viral spread. Utilizing suitable Lyapunov functions, we first establish the existence and uniqueness of the global solution for the HIV model, and then study the pth moment boundedness of the solution. Finally, the unique stationary distribution of the solution to the model is obtained. Numerical simulations are presented to demonstrate validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we consider an age-structured SIR endemic model. The model is formulated from the available literature while adding some new assumptions. In order to control the infection, we consider vaccination as a control variable and a control problem is presented for further analysis. The method of weak derivatives and minimizing sequence argument are used for deriving necessary conditions and existence results. The desired criterion is achieved and sample simulations were presented which shows the effectiveness of the control. [ABSTRACT FROM AUTHOR]

To support sustainable management of apex predator populations, it is important to estimate population size and understand the drivers of population trends to anticipate the consequences of human decisions. Robust population models are needed, which must be based on realistic biological principles and validated with the best available data. A team of international experts reviewed age-structured models of North Atlantic pinniped populations, including Grey seal (Halichoerus grypus), Harp seal (Pagophilus groenlandicus), and Hooded seal (Cystophora cristata). Statistical methods used to fit such models to data were compared and contrasted. Differences in biological assumptions and model equations were driven by the data available from separate studies, including observation methodology and pre-processing. Counts of pups during the breeding season were used in all models, with additional counts of adults and juveniles available in some. The regularity and frequency of data collection, including survey counts and vital rate estimates, varied. Important differences between the models concerned the nature and causes of variation in vital rates (age-dependent survival and fecundity). Parameterisation of age at maturity was detailed and time-dependent in some models and simplified in others. Methods for estimation of model parameters were reviewed and compared. They included Bayesian and maximum likelihood (ML) approaches, implemented via bespoke coding in C, C++, TMB or JAGS. Comparative model runs suggested that as expected, ML-based implementations were rapid and computationally efficient, while Bayesian approaches, which used MCMC or sequential importance sampling, required longer for inference. For grey seal populations in the Netherlands, where preliminary ML-based TMB results were compared with the outputs of a Bayesian JAGS implementation, some differences in parameter estimates were apparent. For these seal populations, further investigations are recommended to explore differences that might result from the modelling framework and model-fitting methodology, and their importance for inference and management advice. The group recommended building on the success of this workshop via continued collaboration with ICES and NAMMCO assessment groups, as well as other experts in the marine mammal modelling community. Specifically, for Northeast Atlantic harp and hooded seal populations, the workshop represents the initial step towards a full ICES benchmark process aimed at revising and evaluating new assessment models.

In this paper, we discuss three different response strategies to a disease outbreak and their economic implications in an age-structured population. We have utilized the classical age structured SIR-model, thus assuming that recovered people will not be infected again. Available resource dynamics is governed by the well-known logistic growth model, in which the reproduction coefficient depends on the disease outbreak spreading dynamics. We further investigate the feedback interaction of the disease spread dynamics and resource growth dynamics with the premise that the quality of treatment depends on the current economic situation. The very inclusion of mortality rates and economic considerations in the same model may be incongruous under certain positions, but in this model, we take a "realpolitik" approach by exploring all of these factors together as it is done in reality. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an age-structured HIV infection model with logistic growth for target cell. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analysing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al., we show that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values. Finally, we perform some numerical simulations to illustrate our results.

In this article, we study the dynamics of a new proposed age-structured population mathematical model driven by a seasonal forcing function that takes into account the variability of the climate. We introduce a generalized force of infection function to study different potential disease outcomes. Using nonlinear analysis tools and differential inequalities theorems, we obtain sufficient conditions that guarantee the existence of a positive periodic solution. Moreover, we provide sufficient conditions that assure the global attractivity of the positive periodic solution. Numerical results corroborate the theoretical results in the sense that the solutions are positive and the periodic solution is a global attractor. This type of models are important, since they take into account the variability of the weather and the impact on some epidemics such as the current COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

As the COVID-19 is still spreading in more than 180 countries, according to WHO. There is a need to understand the dynamics of this infection and predict its the impact on the public health capacity. This work aims to forecast the progress of the disease in three countries from different continents: The United States of America, the United Arab Emirates and Algeria. The existing data shows that the fatality of the disease is high in elderly people and people with comorbidity. Therefore, we consider an age-structured model. Our model also takes into consider two main components of the COVID-19 (a) the number of Infected hospitalized people, therefore, we estimate the number of beds (acute and critical) needed (2) the possible infection of the healthcare personals (HCP). Hence, the model predict the peak time and the number of infectious cases at the peak before and after the implementation of non-pharmaceutical interventions (NPI), and we also compare this finding with case of full lockdown. Finally, we investigate the impact of the shortage of proper personal protective equipment (PPE) on the spread of the disease. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic age‐structured population model with Markovian switching is investigated in a polluted environment. Both the stochastic disturbance of environment and the Markovian switching are incorporated into the model. By Itô formula and several assumptions, the boundedness in the qth moment of exact solutions of model are proved. Furthermore, making use of truncated Euler–Maruyama (EM) method, the strong convergence criterion of numerical approximation in the qth moment is established, and the rate of convergence is estimated. Numerical simulations are carried out to illustrate the theoretical results. Our results indicate that the truncated EM method can be used for stochastic age‐structured population system in a polluted environment. [ABSTRACT FROM AUTHOR]

Abstract Some studies show that latency and relapse, especially the age-dependent latency and relapse, may affect the transmission dynamics of tuberculosis model. Meanwhile, the immigration of infected individuals induces the loss of disease-free steady state and hence no basic reproduction number. In our work, a class of age-structured tuberculosis model with immigration is proposed, where the new individuals can immigrate into the susceptible, latent, infectious and removed compartments. We show that the endemic steady state is unique and globally asymptotically stable by using the Lyapunov functional. Numerical simulations are given to support our theoretical results.

In this paper, allowing for general transmission and recovery times distributions, we proposed an edge-based age-structured-like compartmental model for STIs (EBACMS) in a coupled network. We considered sexual transmissions between men with also heterosexual contacts. Mathematically, we gave the general approach of proving the nonnegativity of solutions for the system coupling ordinary and partial differential equations, which can be applied to all edge-based compartment models. We then analyzed the epidemic threshold ℛ 0 with different distributions which couples the thresholds of the single-layer and bipartite networks in the percolation theory. We also studied the global stability of disease-free equilibrium with ℛ 0 < 1 and the final epidemic size F (the proportion of the population experiencing infection during the epidemic) with ℛ 0 > 1. In addition, numerical simulations indicated that given a fixed exponential transmission distribution, a higher variance (with same mean) in general recovery distribution gives smaller ℛ 0 and F. Sensitivity analysis on ℛ 0 and F in terms of the parameters illustrated that male-to-male transmission routes have a greater impact on ℛ 0 and F than the heterosexual transmission routes for the Markovian transmission process and arbitrary recovery process. The results provide a good theoretical guideline to consider the distributions of real-world STIs. [ABSTRACT FROM AUTHOR]

The periodic behaviors and non-periodic behaviors of recurrent epidemic are discussed by building an SIS model with disease age structure and infectious delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of Hopf bifurcation under the condition where endemic equilibrium is unstable. It implies that the recurrent epidemics will switch between periodic behavior and non-periodic behavior as the parameter values changing when the disease persists in population. The numerical examples are provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an age-structured HIV infection model with logistic growth for target cell. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analysing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al., we show that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values. Finally, we perform some numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, an age-structured prey–predator model with Holling type II functional response incorporating a prey refuge is constructed. Through applying the method of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain, we obtain that the model undergoes a Hopf bifurcation at the interior equilibrium which shows that this model has a non-trivial periodic orbit that bifurcates from the interior equilibrium when bifurcation parameter τ crosses the bifurcation critical value τ 0. Numerical simulations are given to verify the theoretical analysis. The results manifest that the prey refuge has a stabilizing effect, namely, the prey refuge is a significant factor to maintain the balance between the prey population and the predator population. [ABSTRACT FROM AUTHOR]

Highlights • Efficacy of vaccination campaigns differs between endemic and non-endemic settings. • Post-exposure vaccination for tuberculosis is most effective in the United States. • Post-exposure vaccines for TB should be targeted at individuals age 50–70. • Pre-exposure vaccines for TB should be targeted at adolescents or young adults. Abstract According to the World Health Organization, tuberculosis (TB) is the leading cause of death from infectious disease worldwide (WHO, 2017). While there is no effective vaccine against adult pulmonary TB, more than a dozen vaccine candidates are in the clinical trial pipeline. These include both pre-exposure vaccines to prevent initial infections and post-exposure vaccines to prevent reactivation of latent disease. Many epidemiological models have been used to study TB, but most have not included a continuous age structure and the possibility of both pre- and post-exposure vaccination. Incorporating age-dependent death rates, disease properties, and social contact data allows for more realistic modeling of disease spread. We propose a continuous age-structured model for the epidemiology of tuberculosis with pre- and post-exposure vaccination. We use uncertainty and sensitivity analysis to make predictions about the efficacy of different vaccination strategies in a non-endemic setting (United States) and an endemic setting (Cambodia). In particular, we determine optimal age groups to target for pre-exposure and post-exposure vaccination in both settings. We find that the optimal age groups tend to be younger for Cambodia than for the US, and that post-exposure vaccination has a significantly larger effect than pre-exposure vaccination in the US. [ABSTRACT FROM AUTHOR]

This paper concerns modeling the coupled within-host population dynamics of virus and CTL (Cytotoxic T Lymphocyte) immune response. There is substantial evidence that the CTL immune response plays a crucial role in controlling HIV in infected patients. Recent experimental studies have demonstrated that certain CTL variants can recognize HIV infected cells early in the infected cell lifecycle before viral production, while other CTLs only detect viral proteins (epitopes) presented on the surface of infected cells after viral production. The kinetics of epitope presentation and immune recognition can impact the efficacy of the immune response. We extend previous virus models to include cell infection-age structure in the infected cell compartment and immune response killing/activation rates of a PDE-ODE system. We characterize solutions to our system utilizing semigroup theory, determine equilibria and reproduction numbers, and prove stability and persistence results. Numerical simulations show that ``early immune recognition'' precipitates both enhanced viral control and sustained oscillations via a Hopf bifurcation. In addition to inducing oscillatory dynamics, considering immune process rates to be functions of cell infection-age can also lead to coexistence of multiple distinct immune effector populations.

Some studies show that latency and relapse, especially the age-dependent latency and relapse, may affect the transmission dynamics of tuberculosis model. Meanwhile, the immigration of infected individuals induces the loss of disease-free steady state and hence no basic reproduction number. In our work, a class of age-structured tuberculosis model with immigration is proposed, where the new individuals can immigrate into the susceptible, latent, infectious and removed compartments. We show that the endemic steady state is unique and globally asymptotically stable by using the Lyapunov functional. Numerical simulations are given to support our theoretical results. [ABSTRACT FROM AUTHOR]

This articlefocuses on the study of an age-structuredtwo-strain model with super-infection. The explicit expression ofbasic reproduction numbers and the invasion reproduction numberscorresponding to strain one and strain two are obtained. It isshown that the infection-free steady state is globally stable ifthe basic reproductive number $ R_0 $ is below one. Existenceof strain one and strain two exclusive equilibria is established.Conditions for local stability or instability of the exclusive equilibria of thestrain one and strain two are established. Existence ofcoexistence equilibrium is also obtained under the condition that bothinvasion reproduction numbers are larger than one.

The main idea of this work is to present and study the dynamical behavior of an age-dependent SIR endemic model. First, the age-dependent SIR endemic model is formulated from existing SIR epidemic models by adding age-dependent recruitment rate. The behavior of the model is analyzed by using the basic reproductive number R 0 . The stability theory is used for the analysis of disease-free and endemic equilibrium. Finally, finite difference method of characteristics is used to present numerical results for the suggested age-structured endemic model. [ABSTRACT FROM AUTHOR]