Age-structured Model Research Articles

Impact of a potential Chlamydia vaccine in the USA: mathematical modelling analyses

IntroductionChlamydia trachomatis (CT) infection is a global health challenge. New approaches are needed to control CT disease burden.MethodsAn age-structured deterministic mathematical model calibrated to nationally representative population-based data was developed...

Dynamics and asymptotic profiles on an age-structured SIS epidemic model with random diffusion and advection

Dynamics and asymptotic profiles on an age-structured SIS epidemic model with random diffusion and advection

Stability analysis of an age-structured SIR model with nonlocal diffusion and indirect contacts

Stability analysis of an age-structured SIR model with nonlocal diffusion and indirect contacts

Approximating reproduction numbers: a general numerical method for age-structured models.

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.

Stability and optimal control for an age-structured model of periodical cicadas

Stability and optimal control for an age-structured model of periodical cicadas

Collective Defined Contribution Pension with Stochastic Age-structured Models

Collective Defined Contribution Pension with Stochastic Age-structured Models

Stability and Hopf bifurcation for age-structured SVIR epidemic model with different compartment ages and two delays effects

An age-structured SVIR epidemic model with different compartment ages and two delays is investigated. The model is transformed into a non-densely defined abstract Cauchy problem. The basic properties, including the positivity and boundedness of solutions, basic reproduction number R0 and the existence of equilibria, are first derived. The linearized system and characteristic equation at an equilibrium from the corresponding abstract Cauchy problem are also obtained. When R0<1, the local stability of the disease-free equilibrium is proved, and when R0>1 and the two delays vanish, the local stability of the endemic equilibrium is proved. When R0>1, and Assumptions 1 and 2 are satisfied, the existence of Hopf bifurcation are established respectively in the general case with two delays as bifurcation parameters and in three special cases with only one delay as the bifurcation parameter. The results show that disease with the incubation period and the infection period of infection age has very complex dynamical behavior at the endemic equilibrium. Finally, numerical examples validate the theoretical results.

Optimal vaccination ages for emerging infectious diseases under limited vaccine supply.

Rational allocation of limited vaccine resources is one of the key issues in the prevention and control of emerging infectious diseases. An age-structured infectious disease model with limited vaccine resources is proposed to explore the optimal vaccination ages. The effective reproduction number [Formula: see text] of the epidemic disease is computed. It is shown that the reproduction number is the threshold value for eradicating disease in the sense that the disease-free steady state is globally stable if [Formula: see text] and there exists a unique endemic equilibrium if [Formula: see text]. The effective reproduction number is used as an objective to minimize the disease spread risk. Using the epidemic data from the early spread of Wuhan, China and demographic data of Wuhan, we figure out the strategies to distribute the vaccine to the age groups to achieve the optimal vaccination effects. These analyses are helpful to the design of vaccination schedules for emerging infectious diseases.

Modeling and analysis of a multilayer solid tumour with cell physiological age and resource limitations

We study an avascular spherical solid tumour model with cell physiological age and resource constraints in vivo. We divide the tumour cells into three components: proliferating cells, quiescent cells and dead cells in necrotic core. We assume that the division rate of proliferating cells is nonlinear due to the nutritional and spatial constraints. The proportion of newborn tumour cells entering directly into quiescent state is considered, since this proportion can respond to the therapeutic effect of drug. We establish a nonlinear age-structured tumour cell population model. We investigate the existence and uniqueness of the model solution and explore the local and global stabilities of the tumour-free steady state. The existence and local stability of the tumour steady state are studied. Finally, some numerical simulations are performed to verify the theoretical results and to investigate the effects of different parameters on the model.

A mixed-method approach to determining contact matrices in the Cox's Bazar refugee settlement.

Contact matrices are an important ingredient in age-structured epidemic models to inform the simulated spread of the disease between subgroups of the population. These matrices are generally derived using resource-intensive diary-based surveys and few exist in the Global South or tailored to vulnerable populations. In particular, no contact matrices exist for refugee settlements-locations under-served by epidemic models in general. In this paper, we present a novel, mixed-method approach for deriving contact matrices in populations, which combines a lightweight, rapidly deployable survey with an agent-based model of the population informed by census and behavioural data. We use this method to derive the first set of contact matrices for the Cox's Bazar refugee settlement in Bangladesh. To validate our approach, we apply it to the UK population and compare our derived matrices with well-known contact matrices collected using traditional methods. Our findings demonstrate that our mixed-method approach successfully addresses some of the challenges faced by traditional and agent-based approaches to deriving contact matrices. It also shows potential for implementation in resource-constrained environments. This work therefore contributes to a broader aim of developing new methods and mechanisms of data collection for modelling disease spread in refugee and internally displaced person (IDP) settlements and better serving these vulnerable communities.

Modeling the impact of COVID-19 nonpharmaceutical interventions on respiratory syncytial virus transmission in South Africa.

The South African government employed various nonpharmaceutical interventions (NPIs) to reduce the spread of SARS-CoV-2. Surveillance data from South Africa indicates reduced circulation of respiratory syncytial virus (RSV) throughout the 2020-2021 seasons. Here, we use a mechanistic transmission model to project the rebound of RSV in the two subsequent seasons. We fit an age-structured epidemiological model to hospitalization data from national RSV surveillance in South Africa, allowing for time-varying reduction in RSV transmission during periods of COVID-19 circulation. We apply the model to project the rebound of RSV in the 2022 and 2023 seasons. We projected an early and intense outbreak of RSV in April 2022, with an age shift to older infants (6-23 months old) experiencing a larger portion of severe disease burden than typical. In March 2022, government alerts were issued to prepare the hospital system for this potentially intense outbreak. We then assess the 2022 predictions and project the 2023 season. Model predictions for 2023 indicate that RSV activity has not fully returned to normal, with a projected early and moderately intense wave. We estimate that NPIs reduced RSV transmission between 15% and 50% during periods of COVID-19 circulation. A wide range of NPIs impacted the dynamics of the RSV outbreaks throughout 2020-2023 in regard to timing, magnitude, and age structure, with important implications in a low- and middle-income countries (LMICs) setting where RSV interventions remain limited. More efforts should focus on adapting RSV models to LMIC data to project the impact of upcoming medical interventions for this disease.

Overcoming the impossibility of age-balanced harvest

In many countries, sustainability targets for managed fisheries are often expressed in terms of a fixed percentage of the carrying capacity. Despite the appeal of such a simple quantitative target, an unintended consequence may be a significant tilting of the proportions of biomass across different ages, from what they would have been under harvest-free conditions. Within the framework of a widely used age-structured model, we propose a novel quantitative definition of “age-balanced harvest” that considers the age-class composition relative to that of the unfished population. We show that achieving a perfectly age-balanced policy is impossible if we harvest any fish whatsoever. However, every non-trivial harvest policy has a special structure that favours the young. To quantify the degree of age-imbalance, we propose a cross-entropy function. We formulate an optimisation problem that aims to attain an “age-balanced steady state”, subject to adequate yield. We demonstrate that near balanced harvest policies are achievable by sacrificing a small amount of yield. These findings have important implications for sustainable fisheries management by providing insights into trade-offs and harvest policy recommendations.

Cost-effectiveness analysis of typhoid vaccination in Lao PDR

BackgroundTyphoid vaccination has been shown to be an effective intervention to prevent enteric fever and is under consideration for inclusion in the national immunization program in Lao PDR.MethodsA cost-utility analysis was performed using an age-structured static decision tree model to estimate the costs and health outcomes of introducing TCV. Vaccination strategies combined with five delivery approaches in different age groups compared to no vaccination were considered from the societal perspective, using the Gavi price of 1.5 USD per dose. The vaccination program was considered to be cost-effective if the incremental cost-effectiveness ratio was less than a threshold of 1 GDP per capita for Lao PDR, equivalent to USD 2,535 in 2020.ResultsIn the model, we estimated 172.2 cases of enteric fever, with 1.3 deaths and a total treatment cost of USD 7,244, based on a birth cohort of 164,662 births without TCV vaccination that was followed over their lifetime. To implement a TCV vaccination program over the lifetime horizon, the estimated cost of the vaccine and administration costs would be between USD 470,934 and USD 919,186. Implementation of the TCV vaccination program would prevent between 14 and 106 cases and 0.1 to 0.8 deaths. None of the vaccination programs appeared to be cost-effective.ConclusionsInclusion of TCV in the national vaccination program in Lao PDR would only be cost-effective if the true typhoid incidence is 25-times higher than our current estimate.

Modeling vaccination strategies with limited early COVID-19 vaccine access in low- and middle-income countries: A case study of Thailand

Low- and middle-income countries faced significant challenges in accessing COVID-19 vaccines during the early stages of the pandemic. In this study, we utilized an age-structured modeling approach to examine the implications of various vaccination strategies, vaccine prioritization, and vaccine rollout speeds in Thailand, an upper-middle-income country experiencing vaccine shortages during the early stages of the pandemic. The model directly compares the effectiveness of several vaccination strategies, including the heterologous vaccination where CoronaVac (CV) vaccine was administered as the first dose, followed by ChAdOx1 nCoV-19 (AZ) vaccine as the second dose, under varying disease transmission dynamics. We found that the traditional AZ homologous vaccination was more effective than the CV homologous vaccination, regardless of disease transmission dynamics. However, combining CV and AZ vaccines via either parallel homologous or heterologous vaccinations was more effective than relying solely on AZ homologous vaccination. Additionally, prioritizing vaccination for the elderly aged 60 years and above was the most effective way to reduce mortality when community transmission is well-controlled. On the other hand, prioritizing workers aged 20–59 was most effective in lowering COVID-19 cases, irrespective of the transmission dynamics. Lastly, despite the vaccine prioritization strategy, rapid vaccine rollout speeds were crucial in reducing COVID-19 infections and deaths. These findings suggested that in low- and middle-income countries where early access to high-efficacy vaccines might be limited, obtaining any accessible vaccines as early as possible and using them in parallel with other higher-efficacy vaccines might be a better strategy than waiting for and relying solely on higher-efficacy vaccines.

Impact of vaccinations, boosters and lockdowns on COVID-19 waves in French Polynesia

Estimating the impact of vaccination and non-pharmaceutical interventions on COVID-19 incidence is complicated by several factors, including successive emergence of SARS-CoV-2 variants of concern and changing population immunity from vaccination and infection. We develop an age-structured multi-strain COVID-19 transmission model and inference framework to estimate vaccination and non-pharmaceutical intervention impact accounting for these factors. We apply this framework to COVID-19 waves in French Polynesia and estimate that the vaccination programme averted 34.8% (95% credible interval: 34.5–35.2%) of 223,000 symptomatic cases, 49.6% (48.7–50.5%) of 5830 hospitalisations and 64.2% (63.1–65.3%) of 1540 hospital deaths that would have occurred in a scenario without vaccination up to May 2022. We estimate the booster campaign contributed 4.5%, 1.9%, and 0.4% to overall reductions in cases, hospitalisations, and deaths. Our results suggest that removing lockdowns during the first two waves would have had non-linear effects on incidence by altering accumulation of population immunity. Our estimates of vaccination and booster impact differ from those for other countries due to differences in age structure, previous exposure levels and timing of variant introduction relative to vaccination, emphasising the importance of detailed analysis that accounts for these factors.

Mathematical analysis of global dynamics and optimal control of treatment for an age-structured HBV infection model

Evidences show that cell-to-cell infection occurs in HBV infection and is a very efficient way which may lead to more than half of the viral infection. Hence we formulate an HBV infection model with cell-to-cell infection, meanwhile, we incorporate the infection age of infected cells. For dynamic behaviors, we firstly establish the well-posedness and asymptotic smoothness of the model; then show the global threshold dynamical behaviors, which are determined by the reproduction number; and finally perform numerical simulations not only to verify the theoretical results but also to explore effects of cell-to-cell infection on viral load and infection concentration. Our finding is that ignoring the cell-to-cell infection will underestimate the actual HBV infection status. For optimal control of treatment for HBV, we introduce two time-varying control measures and investigate the corresponding optimal control problem. We derive the characteristic expression of the optimal control and discuss effects of control costs and integrated control. The results show that high control cost will not result in better control effectiveness, while integrated optimal control can reach the best control objectives compared with the two single ones. Moreover, infection age can greatly influence HBV infection at the initial stage.

An age-structured differential equations model for transmission dynamics of pneumonia with treatment and nutrition intervention

Pneumonia is the leading infectious disease that threatens the lives of children under five and elders over 65. It is an infection that is commonly caused by Streptococcus pneumoniae. In this study, an age-structured (children and elders) model for pneumonia was formulated and analyzed to determine the impact of treatment and proper nutrition on the transmission dynamics of the disease in the two age groups. The effective reproduction number (Re) was determined using the next-generation method. The disease-free equilibrium point was determined and found locally and globally asymptotically stable if Re<1. Sensitivity analysis of the model parameters was performed using the normalized forward sensitivity index method, and the findings show that transmission rates are the most positive parameters to the effective reproduction number, while proper nutrition was the most negatively sensitive parameter. Additionally, numerical simulations were performed, and it was observed that the combination of proper nutrition and treatment was more effective in reducing the number of pneumonia-infected individuals. The study encourages the joint use of proper nutrition and treatment to control pneumonia transmission among children and elders, especially in the developing world, where economic constraints, infrastructure, and distribution challenges limit vaccine availability.

Global asymptotic stability for Gurtin-MacCamy’s population dynamics model

In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker’s type of birth function. This model is a hyperbolic partial differential equation with a nonlinear and nonlocal boundary condition. We prove a uniform persistence result for the semiflow generated by this model. We obtain the existence of global attractors and we prove the global asymptotic stability of the positive equilibrium by using a suitable Lyapunov functional. Furthermore, we prove that our global asymptotic stability result is sharp, in the sense that Hopf bifurcation may occur as close as we want from the region global stability in the space of parameter.

Pharmacodynamic Age Structured Population Model For Cell Trafficking

ObjectivesCell trafficking encompasses movement of the immune system cells (e.g., granulocytes, lymphocytes) between the blood and the extravascular tissues (e.g., lymph nodes). Corticosteroids are known to suppress cell trafficking. The age-structured cell population models introduce the transit time as a structure that allows one to quantify the distribution of times the immune cells spend in the blood and the extravascular tissues. The objective of this work is to develop an age-structured cell population model describing drug effects on cell trafficking and to implement the model in pharmacometric software to enable parameter estimation and simulations. MethodsWe adopted the well-known McKendrick age-structured population model to describe the age distributions in two cell populations: blood cells and cells in the extravascular space. The hazard of cell recirculation from the extravascular tissues was age dependent and described by the Weibull function with the shape ν and scale β parameters. The drug effect on cell trafficking was modeled as the product of the Emax function of the drug plasma concentration and the Weibull hazard. The model was implemented in NONMEM 7.5.1. The model was applied to the basophil data in 34 healthy subjects who received a single intramuscular or oral dose of 6 mg dexamethasone (DEX). A recently published pharmacokinetic model was applied to describe DEX plasma concentration. Typical values of parameter estimates were further used to simulate the DEX effect of the basophil mean transit time in the extravascular tissues. ResultsSimulations of basophil time courses for varying ν demonstrated that the rebound in the blood count data following drug administration is only possible for ν >1. The estimates of model parameters were ν = 3.02, β = 0.00863 1/h, and IC50 = 7.47 ng/mL. The calculated baseline mean transit times of basophils in the blood 7.2 h and extravascular tissues 104.9 h agree with the values reported in the literature. ConclusionsWe introduced an age-structured population model to describe cell trafficking between the blood and extravascular tissues. The model was adopted to account for the inhibitory drug effect on the cell recirculation. We showed that the age structure is essential to explain the rebound observed in the blood count response to a single dose drug administration. The model was validated using the basophil responses to DEX treatment in healthy subjects.

Impact and cost-effectiveness of measles vaccination through microarray patches in 70 low-income and middle-income countries: mathematical modelling and early-stage economic evaluation

BackgroundMicroarray patches (MAPs) are a promising technology being developed to reduce barriers to vaccine delivery based on needles and syringes (N&S). To address the evidence gap on the public health...