Age-structured Model Research Articles

Frequently Hypercyclic Semigroup Generated by Some Partial Differential Equations with Delay Operator

In this paper, under appropriate hypotheses, we have the existence of a solution semigroup of partial differential equations with delay operator. These equations are used to describe time–age-structured cell cycle model. We also prove that the solution semigroup is a frequently hypercyclic semigroup.

Demographic models predict end-Pleistocene arrival and rapid expansion of pre-agropastoralist humans in Cyprus

The antiquity of human dispersal into Mediterranean islands and ensuing coastal adaptation have remained largely unexplored due to the prevailing assumption that the sea was a barrier to movement and that islands were hostile environments to early hunter-gatherers [J. F. Cherry, T. P. Leppard, J. Isl. Coast. Archaeol. 13, 191-205 (2018), 10.1080/15564894.2016.1276489]. Using the latest archaeological data, hindcasted climate projections, and age-structured demographic models, we demonstrate evidence for early arrival (14,257 to 13,182 calendar years ago) to Cyprus and predicted that large groups of people (~1,000 to 1,375) arrived in 2 to 3 main events occurring within <100 y to ensure low extinction risk. These results indicate that the postglacial settlement of Cyprus involved only a few large-scale, organized events requiring advanced watercraft technology. Our spatially debiased and Signor-Lipps-corrected estimates indicate rapid settlement of the island within <200 y, and expansion to a median of 4,000 to 5,000 people (0.36 to 0.46 km-2) in <11 human generations (<300 y). Our results do not support the hypothesis of inaccessible and inhospitable islands in the Mediterranean for pre-agropastoralists, agreeing with analogous conclusions for other parts of the world [M. I. Bird et al., Sci. Rep. 9, 8220 (2019), 10.1038/s41598-019-42946-9]. Our results also highlight the need to revisit these questions in the Mediterranean and test their validity with new technologies, field methods, and data. By applying stochastic models to the Mediterranean region, we can place Cyprus and large islands in general as attractive and favorable destinations for paleolithic peoples.

Coding Optimization for an Ecological non-linear Age-structured Fish Population Model with a Shepherd Recruitment Function

The study of the optimally density-regulated recruitment plays a crucial role in the overall management and determining of fishing efforts of marine fish populations. This paper will develop a Matlab code can determine what an optimal recruitment density regulation strategy would be for the un-fished population and what it changes to when fishing efforts are applied. This code can determine threshold values used to avoid fisheries from collapsing. The code will be applied to the Gulf of California Pacific sardine (Sardinops caeruleus) population. An age structured design with a Shepherd density regulating stock-recruitment function is used in this study. In this work, the parameter which is varied is captured in the Shepherd recruitment function and is associated with behavioral interventions such as selecting different drift routes and clumping on resources that will increase egg-larvae survival to the recruitment stage. A detailed background study of other models is explored, then a derivation of the Shepherd recruitment model is developed from the traditional discrete model. A special MATLAB code is then developed to illustrate the pair-wise invasive plots for the model structures. The code is for theoretical analysis of fish population models.

Vaccination games and imitation dynamics with age structure combining perceived payoffs and media information

We propose an age-structured model based on game theory to investigate the dynamics of imitation in vaccination decisions. In our model, the rate at which individuals switch vaccination strategies is proportional to the perceived payoffs and media information. We analyze the existence and local stability of equilibria and demonstrate the possibility of Hopf bifurcation. Additionally, we establish the global stability of boundary equilibria and the persistence of the disease. The theoretical results are supported by numerical simulations. This model can be applied to study vaccination behavior among individuals of different ages and infectious disease stages, providing insights for the formulation of effective public health policies.

Numerical analysis of a nonlinear age-structured HBV model with saturated incidence and spatial diffusion

In this paper, the numerical properties of a nonlinear age-structured hepatitis B virus model with saturated incidence and spatial diffusion are studied. Applying linearly implicit Euler method in time integration, a numerical scheme which can preserve the biological meanings is constructed. The convergence of the numerical solution in finite time is explored. In stability analysis, a threshold is proposed, which is called numerical basic reproduction number and denoted by R0h. It is proved that the numerical solution is locally asymptotically stable at the disease-free equilibrium when R0h<1. Moreover, it is proved the numerical basic reproduction number converges to the exact basic reproduction number of the model with first order accuracy. Furthermore, it is shown that a numerical space independent equilibrium exists and is asymptotically stable if R0h>1, which implies the threshold stability of the model can be preserved by numerical solution proposed. Eventually, our conclusions are tested through numerical experiments.

Dynamical analysis of an age-structured SEIR model with relapse

Dynamical analysis of an age-structured SEIR model with relapse

Age validation of yellowfin tuna Thunnus albacares in the Indian Ocean using post-peak bomb radiocarbon chronologies

Yellowfin tuna Thunnus albacares stock assessments use age-structured models; therefore, accurate methods for ageing the catch are required. Age estimation techniques need to be validated at the population level to ensure accuracy. However, otolith-based age estimates of yellowfin tuna have never been validated in the Indian Ocean. The current study provides the first age validation for Indian Ocean yellowfin tuna using the post-peak decline period of the bomb radiocarbon (14C) chronometer. A 14C reference chronology based on accelerator mass spectrometry assays of known-age yellowfin tuna otoliths was consistent with published regional coral records, with all showing similar rates of decline during the 2000 to 2019 study period. After back-calculating the birth years of sub-adult and adult yellowfin tuna from otolith increment counts, Δ14C values measured in the early growth portion of the otolith were compared with the observed decline slope of the reference chronology. There were no significant differences between the birth years of validation and reference samples, supporting the otolith increment age determination methodology between the ages of 2.2 and 10.5 yr. The validation of age and growth estimates is expected to benefit assessment models for Indian Ocean yellowfin tuna. We recommend that otoliths from large fish continue to be collected to expand the validation to older fish. Greater precision in the validation results will also require a larger reference chronology.

Numerical analysis of age-structured HIV model with general transmission mechanism

In this paper, we discuss the numerical representation of the linearly implicit Euler method for an age-structured HIV infection model with a general transmission mechanism. We first define the basic reproduction number of the continuous model, and present the stability results of the equilibriums. For the numerical process, we establish the solvability of the system and the non-negativity and convergence of numerical solutions. In the analysis of the long-term dynamical behavior, this paper mainly focus on the existence of the infection equilibrium determined by the numerical reproduction number R0Δt. To overcome the difficulty caused by the complexity of epidemic transmission mechanisms, the 1-order convergence analysis of numerical basic reproduction numbers R0Δt is implemented by using the properties of the fundamental solution matrix. By a comparison principle, we show that the disease-free equilibrium is globally asymptotically stable if R0Δt<1. Moreover, for R0Δt>1, a unique numerical endemic equilibrium exists, which converges to the exact one, is locally asymptotically stable. Hence, numerical processes visually represent the dynamic properties of nonlinear age-structured HIV models. Finally, some numerical experiments demonstrate the verification and the efficiency of our results.

Evaluation of age-structured vaccination strategies forcurbing the disease spread.

Age structure is one of the crucial factors in characterizing the heterogeneous epidemic transmission. Vaccination is regarded as an effective control measure for prevention and control epidemics. Due to the shortage of vaccine capacity during the outbreak of epidemics, how to design vaccination policy has become an urgent issue in suppressing the disease transmission. In this paper, we make an effort to propose an age-structured SVEIHR model with the disease-caused death to take account of dynamics of age-related vaccination policy for better understanding disease spread and control. We present an explicit expression of the basic reproduction number , which determines whether or not the disease persists, and then establish the existence and stability of endemic equilibria under certain conditions. Numerical simulations are illustrated to show that the age-related vaccination policy has a tremendous influence on curbing the disease transmission. Especially, vaccination of people over 65 is better than for people aged 21-65 in terms of rapid eradication of the disease in Italy.

Ergodic stationary distribution of age-structured HBV epidemic model with standard incidence rate

Ergodic stationary distribution of age-structured HBV epidemic model with standard incidence rate

A note on the compactness of the resolvent of the age-diffusion operator

The generator of the semigroup associated with linear age-structured population models including spatial diffusion is shown to have compact resolvent.

Global analysis of an age-structured tuberculosis model with an application to Jiangsu, China.

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 . When , the disease-free equilibrium is globally asymptotically stable, which means that TB epidemic will die out; When , the disease-free equilibrium is globally attractive; there exists a unique endemic equilibrium and the endemic equilibrium is globally attractive when . We estimate that the basic reproduction number (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.

Evaluation of Strategies for Transitioning to Annual SARS-CoV-2 Vaccination Campaigns in the United States.

The U.S. Food and Drug Administration has proposed administering annual SARS-CoV-2 vaccines. To evaluate the effectiveness of an annual SARS-CoV-2 vaccination campaign, quantify the health and economic benefits of a second dose provided to children younger than 2 years and adults aged 50 years or older, and optimize the timing of a second dose. An age-structured dynamic transmission model. United States. A synthetic population reflecting demographics and contact patterns in the United States. Vaccination against SARS-CoV-2 with age-specific uptake similar to that of influenza vaccination. Incidence, hospitalizations, deaths, and direct health care cost. The optimal timing between the first and second dose delivered to children younger than 2 years and adults aged 50 years or older in an annual vaccination campaign was estimated to be 5 months. In direct comparison with a single-dose campaign, a second booster dose results in 123 869 fewer hospitalizations (95% uncertainty interval [UI], 121 994 to 125 742 fewer hospitalizations) and 5524 fewer deaths (95% UI, 5434 to 5613 fewer deaths), averting $3.63 billion (95% UI, $3.57 billion to $3.69 billion) in costs over a single year. Population immunity is subject to degrees of immune evasion for emerging SARS-CoV-2 variants. The model was implemented in the absence of nonpharmaceutical interventions and preexisting vaccine-acquired immunity. The direct health care costs of SARS-CoV-2, particularly among adults aged 50 years or older, would be substantially reduced by administering a second dose 5 months after the initial dose. Natural Sciences and Engineering Research Council of Canada, Notsew Orm Sands Foundation, National Institutes of Health, Centers for Disease Control and Prevention, and National Science Foundation.

Smooth center-stable/unstable manifolds and foliations of stochastic evolution equations with non-dense domain

The current paper is devoted to the asymptotic behavior of a class of stochastic PDE. More precisely, with the help of the theory of integrated semigroups and a crucial estimate of the random Stieltjes convolution, we study the existence and smoothness of center-unstable invariant manifolds and center-stable foliations for a class of stochastic PDE with non-dense domain through the Lyapunov-Perron method. Finally, we give two examples, a stochastic age-structured model and a stochastic parabolic equation, to illustrate our results.

Exploring the Pareto front of multi-objective COVID-19 mitigation policies using reinforcement learning

Infectious disease outbreaks can have a disruptive impact on public health and societal processes. As decision-making in the context of epidemic mitigation is multi-dimensional hence complex, reinforcement learning in combination with complex epidemic models provides a methodology to design refined prevention strategies. Current research focuses on optimizing policies with respect to a single objective, such as the pathogen’s attack rate. However, as the mitigation of epidemics involves distinct, and possibly conflicting, criteria (i.a., mortality, morbidity, economic cost, well-being), a multi-objective decision approach is warranted to obtain balanced policies. To enhance future decision-making, we propose a deep multi-objective reinforcement learning approach by building upon a state-of-the-art algorithm called Pareto Conditioned Networks (PCN) to obtain a set of solutions for distinct outcomes of the decision problem. We consider different deconfinement strategies after the first Belgian lockdown within the COVID-19 pandemic and aim to minimize both COVID-19 cases (i.e., infections and hospitalizations) and the societal burden induced by the mitigation measures. As such, we connected a multi-objective Markov decision process with a stochastic compartment model designed to approximate the Belgian COVID-19 waves and explore reactive strategies. As these social mitigation measures are implemented in a continuous action space that modulates the contact matrix of the age-structured epidemic model, we extend PCN to this setting. We evaluate the solution set that PCN returns, and observe that it explored the whole range of possible social restrictions, leading to high-quality trade-offs, as it captured the problem dynamics. In this work, we demonstrate that multi-objective reinforcement learning adds value to epidemiological modeling and provides essential insights to balance mitigation policies.

Cost-Effectiveness of Human Papillomavirus Vaccination in the UK: Two Versus Single-Dose of Nonavalent HPV Vaccination

IntroductionThe UK implemented a single-dose HPV vaccination policy in September 2023, aiming for sustained protection, better vaccine coverage, and reduced healthcare costs. This research assesses the cost-effectiveness of both one-dose and two-dose schedules from a healthcare perspective. MethodsUsing an age-structured dynamic model, the study analyzed long-term health and economic outcomes of these two different vaccination approaches. It focused on the effects of vaccinating 12- to 13-year-olds with the 9-valent HPV vaccine in either single-dose or two-dose regimens from 2023 to 2093. The analysis, conducted in 2023–2024, explored different immunity durations (10, 30 years, or lifetime) and efficacy levels for the single-dose strategy. ResultsThe study indicated that in the UK, vaccinating 12- to 13-year-olds with a two-dose regimen is not considered cost-effective compared to the single-dose option, assumed to be 90% as effective for ten years. The incremental cost-effectiveness ratios (ICERs) for two doses ranged from £230,903 to £1,082,916 per quality-adjusted life year (QALY), significantly exceeding the UK's £20,000/QALY willingness-to-pay threshold. Over 70 years, a switch from a two-dose to a single-dose vaccination schedule could potentially lead to savings of over £1,073 million in the healthcare system. Furthermore, the single-dose regimen was cost-effective compared to no vaccination, with an ICER below £2,040/QALY. ConclusionsThe study affirms the cost-effectiveness of the UK's single-dose HPV vaccine, in sync with its September 2023 policy shift. The shift not only provides financial benefits but also simplifies vaccine administration, strategically reducing HPV's epidemiological and economic impacts.

Dynamics of a generalized age-structured model for HBV infection with capsids in presence of two treatments

Dynamics of a generalized age-structured model for HBV infection with capsids in presence of two treatments

INVESTIGATION ON PREDICTING FAMILY PLANNING AND WOMEN’S AND CHILDREN’S HEALTH EFFECTS ON BANGLADESH BY CONDUCTING AGE STRUCTURE POPULATION MODEL

Bangladesh has a higher population density than most other nations in the world. This project aims to evaluate the effects of experimental family planning and maternal and child health. Bangladesh saw changes in the use of contraceptives, the continuation of contraception, fertility, and infant and child mortality between 2012 and 2022. The project's current goal is to guarantee improved family health. To satisfy the changing needs and priorities of families and to provide better health for all, this paper has proposed several novel initiatives, such as enhanced health and family planning services, and enhancing maternal and child health. The goal of this project is to improve the health of women and children through family planning using an age-structured population model. It also covers the graphical presentation of the data using programs like Matlab, Mathematica, Excel, and others.

A network-based model to assess vaccination strategies for the COVID-19 pandemic by using Bayesian optimization

In this paper we build a network-based model to evaluate and compare vaccination plans in order to find the optimal strategies. The age-structured model is designed to take into account the comorbidity status and vaccination hesitancy of the population. The network-based model is calibrated to reported infected cases and deaths in the USA in order to obtain an approximated realistic scenario to test the vaccination strategies. We adapt an algorithm that is based on Bayesian optimization over permutation spaces with heuristics in order to deal with the discrete space of the vaccination strategies. We also developed an ad-hoc randomized algorithm which has a higher computational cost. Both algorithms provide similar patterns of the best found vaccination strategies. We find that these best vaccination plans prioritize the age-groups 40–59 and 60–69 years old, both with comorbidities. This result shows the highly nonlinear complexity related to the problem and its dependence on social contacts and case fatality rates. The developed network-based model adapts well to the uncertainty and heterogeneity of the real world situation and allows us to assess the efficacy of many vaccination strategies. The stochastic nature of the simulations enables us to explore additional potential scenarios and the findings offer useful information for developing vaccination plans for other future potential pandemics.

An analytically tractable, age-structured model of the impact of vector control on mosquito-transmitted infections.

Vector control is a vital tool utilised by malaria control and elimination programmes worldwide, and as such it is important that we can accurately quantify the expected public health impact of these methods. There are very few previous models that consider vector-control-induced changes in the age-structure of the vector population and the resulting impact on transmission. We analytically derive the steady-state solution of a novel age-structured deterministic compartmental model describing the mosquito feeding cycle, with mosquito age represented discretely by parity-the number of cycles (or successful bloodmeals) completed. Our key model output comprises an explicit, analytically tractable solution that can be used to directly quantify key transmission statistics, such as the effective reproductive ratio under control, Rc, and investigate the age-structured impact of vector control. Application of this model reinforces current knowledge that adult-acting interventions, such as indoor residual spraying of insecticides (IRS) or long-lasting insecticidal nets (LLINs), can be highly effective at reducing transmission, due to the dual effects of repelling and killing mosquitoes. We also demonstrate how larval measures can be implemented in addition to adult-acting measures to reduce Rc and mitigate the impact of waning insecticidal efficacy, as well as how mid-ranges of LLIN coverage are likely to experience the largest effect of reduced net integrity on transmission. We conclude that whilst well-maintained adult-acting vector control measures are substantially more effective than larval-based interventions, incorporating larval control in existing LLIN or IRS programmes could substantially reduce transmission and help mitigate any waning effects of adult-acting measures.