Age-structured Model Research Articles

Global dynamics on a class of age-infection structured cholera model with immigration

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.

Optimal control and stability analysis of an age-structured SEIRV model with imperfect vaccination.

Vaccination programs are crucial for reducing the prevalence of infectious diseases and ultimately eradicating them. A new age-structured SEIRV (S-Susceptible, E-Exposed, I-Infected, R-Recovered, V-Vaccinated) model with imperfect vaccination is proposed. After formulating our model, we show the existence and uniqueness of the solution using semigroup of operators. For stability analysis, we obtain a threshold parameter $ R_0 $. Through rigorous analysis, we show that if $ R_0 < 1 $, then the disease-free equilibrium point is stable. The optimal control strategy is also discussed, with the vaccination rate as the control variable. We derive the optimality conditions, and the form of the optimal control is obtained using the adjoint system and sensitivity equations. We also prove the uniqueness of the optimal controller. To visually illustrate our theoretical results, we also solve the model numerically.

Asymptotic analysis of an age-structured predator-prey model with ratio-dependent Holling Ⅲ functional response and delays

&lt;p style='text-indent:20px;'&gt;This paper studies the dynamical behavior of a radio-dependent predator-prey model with age structure and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the conditions for existence of the positive equilibrium point are derived. Then, through determining the distribution of eigenvalues, the globally asymptotic stability of the boundary equilibrium and the locally asymptotic stability for the positive equilibrium are obtained, respectively. In addition, it is also shown that a non-trivial periodic oscillation phenomenon through Hopf bifurcation appears under some conditions. Finally, some numerical examples are provided to illustrate the obtained results.&lt;/p&gt;

Cost-Effectiveness of Age-Expanding Strategy of Latent Tuberculosis Infection Treatment in Household Contacts in South Korea.

The strategy of latent tuberculosis infection (LTBI) treatment in household tuberculosis (TB) contacts has been expanding in South Korea. However, there is little evidence of the cost-effectiveness of LTBI treatment in patients over 35 years of age. This study aimed to evaluate the cost-effectiveness of LTBI treatment among household TB contacts in different age groups in South Korea. An age-structured model of TB was developed based on the reports from the Korea Disease Control and Prevention Agency and the National Health Insurance Service. Quality-adjusted life-years (QALY) and the averted number of TB-related deaths were estimated along with discounted costs for a measure of incremental cost-effectiveness ratios. The number of cumulative active TB cases would decrease by 1564 and 7450 under the scenario of LTBI treatment for those aged <35 years and <70 years, respectively, relative to the no-treatment scenario. The treatment strategies for patients aged 0 to <35 years, <55 years, <65 years, and <70 years would add 397, 1482, 3782, and 8491 QALYs at a cost of $660, $5930, $4560, and $2530, respectively, per QALY. For the averted TB-related deaths, LTBI treatment targeting those aged 0 to <35 years, <55 years, <65 years, and <70 years would avert 7, 89, 155, and 186 deaths at a cost of $35900, $99200, $111100, and $115700 per deaths, respectively, in 20 years. The age-specific expansion policy of LTBI treatment not only for those under 35 years of age but also for those under 65 years of age among household contacts was cost-effective in terms of QALYs and averted TB deaths.

Age-specific contribution of contacts to transmission of SARS-CoV-2 in Germany

Current estimates of pandemic SARS-CoV-2 spread in Germany using infectious disease models often do not use age-specific infection parameters and are not always based on age-specific contact matrices of the population. They also do usually not include setting- or pandemic phase-based information from epidemiological studies of reported cases and do not account for age-specific underdetection of reported cases. Here, we report likely pandemic spread using an age-structured model to understand the age- and setting-specific contribution of contacts to transmission during different phases of the COVID-19 pandemic in Germany. We developed a deterministic SEIRS model using a pre-pandemic contact matrix. The model was optimized to fit age-specific SARS-CoV-2 incidences reported by the German National Public Health Institute (Robert Koch Institute), includes information on setting-specific reported cases in schools and integrates age- and pandemic period-specific parameters for underdetection of reported cases deduced from a large population-based seroprevalence studies. Taking age-specific underreporting into account, younger adults and teenagers were identified in the modeling study as relevant contributors to infections during the first three pandemic waves in Germany. For the fifth wave, the Delta to Omicron transition, only age-specific parametrization reproduces the observed relative and absolute increase in pediatric hospitalizations in Germany. Taking into account age-specific underdetection did not change considerably how much contacts in schools contributed to the total burden of infection in the population (up to 12% with open schools under hygiene measures in the third wave). Accounting for the pandemic phase and age-specific underreporting is important to correctly identify those groups of the population in which quarantine, testing, vaccination, and contact-reduction measures are likely to be most effective and efficient. Age-specific parametrization is also highly relevant to generate informative age-specific output for decision makers and resource planers.

A hierarchical age-structured model of optimal vermin management by contraception.

Taking the reproduction law of vermin into consideration, we formulate a hierarchical age-structured model to describe the optimal management of vermin by contraception control. It is shown that the model is well-posed, and the solution has a separable form. The existence of optimal management policy is established via a minimizing sequence and the use of compactness, while the structure of optimal strategy is obtained by using an adjoint system and normal cones. To show the compactness, we use the Fréchet-Kolmogorov theorem and its generalization. To construct the adjoint system, we give some continuity results. Finally, an illustrative example is given.

Preparing for the upcoming 2022/23 influenza season: A modelling study of the susceptible population in Australia, France, Germany, Italy, Spain and the United Kingdom

We analysed the influenza epidemic that occurred in Australia during the 2022 winter using an age-structured dynamic transmission model, which accounts for past epidemics to estimate the population susceptibility to an influenza infection. We applied the same model to five European countries. Our analysis suggests Europe might experience an early and moderately large influenza epidemic. Also, differences may arise between countries, with Germany and Spain experiencing larger epidemics, than France, Italy and the United Kingdom, especially in children.

Estimating economic-based target reference points for key species in multi-species multi-métier fisheries

Consideration of economic outcomes is commonplace in most fisheries management systems globally, although only a few jurisdictions have adopted an economic objective as the primary target for fisheries management. Such an objective has been adopted for Australia's federally managed fisheries, with maximum economic yield (MEY) identified as the primary management objective. Correspondingly, target reference points defined in terms of biomass (i.e., BMEY) are used in harvest control rules. In the absence of explicit BMEY estimates, proxy estimates based on maximum sustainable yield (i.e., BMSY) are used. Identifying BMEY in multi-species fisheries is complicated as most stock assessments are undertaken at the individual species level, but economic activity occurs across species. This is further complicated when different fishing activities using different fishing gears and targeting practices (i.e., métiers) are present in a fishery. We employ an age-structured bioeconomic model to estimate BMEY for key species in a multi-species, multi-métier fishery. We find that optimal biomass levels are substantially higher than those assumed under the current proxy-based system, and that the economic targets are sensitive to prices and fishing costs, both of which change over time.

Identifying susceptibility of children and adolescents to the Omicron variant (B.1.1.529)

BackgroundThe Omicron variant (B.1.1.529) is estimated to be more transmissible than previous strains of SARS-CoV-2 especially among children, potentially resulting in croup which is a characteristic disease in children. Current coronavirus disease 2019 (COVID-19) cases among children might be higher because (i) school-aged children have higher contact rates and (ii) the COVID-19 vaccination strategy prioritizes the elderly in most countries. However, there have been no reports confirming the age-varying susceptibility to the Omicron variant to date.MethodsWe developed an age-structured compartmental model, combining age-specific contact matrix in South Korea and observed distribution of periods between each stage of infection in the national epidemiological investigation. A Bayesian inference method was used to estimate the age-specific force of infection and, accordingly, age-specific susceptibility, given epidemic data during the third (pre-Delta), fourth (Delta driven), and fifth (Omicron driven) waves in South Korea. As vaccine uptake increased, individuals who were vaccinated were excluded from the susceptible population in accordance with vaccine effectiveness against the Delta and Omicron variants, respectively.ResultsA significant difference between the age-specific susceptibility to the Omicron and that to the pre-Omicron variants was found in the younger age group. The rise in susceptibility to the Omicron/pre-Delta variant was highest in the 10–15 years age group (5.28 times [95% CI, 4.94–5.60]), and the rise in susceptibility to the Omicron/Delta variant was highest in the 15–19 years age group (3.21 times [95% CI, 3.12–3.31]), whereas in those aged 50 years or more, the susceptibility to the Omicron/pre-Omicron remained stable at approximately twofold.ConclusionsEven after adjusting for contact pattern, vaccination status, and waning of vaccine effectiveness, the Omicron variant of SARS-CoV-2 tends to propagate more easily among children than the pre-Omicron strains.

Modelling and prevention of crime using age-structure and law enforcement

Every community experiences crime, therefore being aware of it is essential. It is natural to characterize individuals based on age when we consider the modelling of crime, as we do not expect a child to commit a crime. Also, a particular age group may be more prone to commit crimes. Keeping this in mind, we consider an age-structured model of the criminal and noncriminal-minded population in a society. The criminal-minded population is further divided into three categories. We develop a model and study the interaction between them. One crucial factor which we study is the effect of law enforcement. The global existence of steady state is shown using the method of induction on the real line. We check the stability of steady states by constructing appropriate Lyapunov functions. We have established the stability of the crime-free equilibrium. This equilibrium is more important as every society wants to achieve it. We also show the existence of forward bifurcation. It is interesting to see that the outcomes are very natural and enhance our understanding of such classes. Numerical simulations are also given for better illustration.

Mathematical modeling and investigation on the role of demography and contact patterns in social distancing measures effectiveness in COVID-19 dissemination.

In this article, we investigate the importance of demography and contact patterns in determining the spread of COVID-19 and to the effectiveness of social distancing policies. We investigate these questions proposing an augmented epidemiological model with an age-structured model, with the population divided into susceptible (S), exposed (E), asymptomatic infectious (A), hospitalized (H), symptomatic infectious (I) and recovered individuals (R), to simulate COVID-19 dissemination. The simulations were carried out using six combinations of four types of isolation policies (work restrictions, isolation of the elderly, community distancing and school closures) and four representative fictitious countries generated over alternative demographic transition stage patterns (aged developed, developed, developing and least developed countries). We concluded that the basic reproduction number depends on the age profile and the contact patterns. The aged developed country had the lowest basic reproduction number ($R0=1.74$) due to the low contact rate among individuals, followed by the least developed country ($R0=2.00$), the developing country ($R0=2.43$) and the developed country ($R0=2.64$). Because of these differences in the basic reproduction numbers, the same intervention policies had higher efficiencies in the aged and least developed countries. Of all intervention policies, the reduction in work contacts and community distancing were the ones that produced the highest decrease in the $R0$ value, prevalence, maximum hospitalization demand and fatality rate. The isolation of the elderly was more effective in the developed and aged developed countries. The school closure was the less effective intervention policy, though its effects were not negligible in the least developed and developing countries.

Dynamical analysis for an age-structured model of eating disorders

Dynamical analysis for an age-structured model of eating disorders

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model.

The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

Accounting for transgenerational effects of toxicant exposure in population models alters the predicted long-term population status.

Acute environmental stressors such as short-term exposure to pollutants can have lasting effects on organisms, potentially impacting future generations. Parental exposure to toxicants can result in changes to the epigenome (e.g., DNA methylation) that are passed down to subsequent, unexposed generations. However, it is difficult to gauge the cumulative population-scale impacts of epigenetic effects from laboratory experiments alone. Here, we developed a size- and age-structured delay-coordinate population model to evaluate the long-term consequences of epigenetic modifications on population sustainability. The model emulated changes in growth, mortality, and fecundity in the F0, F1, and F2 generations observed in experiments in which larval Menidia beryllina were exposed to environmentally relevant concentrations of bifenthrin (Bif), ethinylestradiol (EE2), levonorgestrel (LV), or trenbolone (TB) in the parent generation (F0) and reared in clean water up to the F2 generation. Our analysis suggests potentially dramatic population-level effects of repeated, chronic exposures of early-life stage fish that are not captured by models not accounting for those effects. Simulated exposures led to substantial declines in population abundance (LV and Bif) or near-extinction (EE2 and TB) with the exact trajectory and timeline of population decline dependent on the combination of F0, F1, and F2 effects produced by each compound. Even acute one-time exposures of each compound led to declines and recovery over multiple years due to lagged epigenetic effects. These results demonstrate the potential for environmentally relevant concentrations of commonly used compounds to impact the population dynamics and sustainability of an ecologically relevant species and model organism.

Variability, skipped breeding and heavy-tailed dynamics in an Antarctic seabird.

The population dynamics of many colonially breeding seabirds are characterized by large interannual fluctuations that cannot be explained by environmental conditions alone. This variation may be particularly confounded by the use of skipped breeding by seabirds as a life-history strategy, which directly impacts the number of breeding pairs and may affect the accuracy of breeding abundance as a metric of population health. Additionally, large fluctuations in time series may suggest that the underlying population dynamics are heavy tailed, allowing for a higher likelihood of extreme events than expected under Gaussian dynamics. Here, we investigated the effect of demography on time series for abundance of the Adélie penguin Pygoscelis adeliae and explored the occurrence of heavy-tailed dynamics in observed Adélie time series. We focus this study on the Adélie penguin as it is an important bellwether species long used to track the impacts of climate change and fishing on the Southern Ocean ecosystem and shares life-history traits with many colonial seabirds. We quantified the impacts of demographic rates, including skipped breeding, on time series of Adélie abundance simulated using an age-structured model. We also used observed time series of Adélie breeding abundance at all known Antarctic colonies to classify distributions for abundance as Gaussian or non-Gaussian heavy tailed. We then identified the cause of such heavy-tailed dynamics in simulated time series and linked these to spatial patterns in Adélie food resource variability. We found that breeding propensity drives observed breeding fluctuations more than any other vital rate, with high variability in skipped breeding decoupling true abundance from observed breeding abundance. We also found several Antarctic regions characterized by heavy-tailed dynamics in abundance. These regions were often also characterized by high variability in zooplankton availability. In simulated time series, heavy-tailed dynamics were strongly linked to high variability in adult survival. Our results illustrate that stochastic variability in abundance dynamics, particularly the presence of variable rates of skipped breeding, can challenge our interpretation of fluctuations in abundance through time and obscure the relationship between key environmental drivers and population abundance.

Mathematical Analysis and Simulation of an Age-Structured Model with Two-Patch and an Uncontrolled Migration: Application to Tuberculosis

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.

Predicted effectiveness of vaccines and extended half-life monoclonal antibodies against RSV hospitalizations in children

Several vaccines and extended half-life monoclonal antibodies (mAbs) against respiratory syncytial virus (RSV) have shown promise in clinical trials. We used age-structured transmission models to predict the possible impact of various RSV prevention strategies including maternal immunization, live-attenuated vaccines, and long-lasting mAbs. Our results suggest that maternal immunization and long-lasting mAbs are likely to be highly effective in preventing RSV hospitalizations in infants under 6 months of age, averting more than half of RSV hospitalizations in neonates. Live-attenuated vaccines could reduce RSV hospitalizations in vaccinated age groups and are also predicted to have a modest effect in unvaccinated age groups because of disruptions to transmission. Compared to year-round vaccination, a seasonal vaccination program at the country level provides at most a minor advantage regarding efficiency. Our findings highlight the substantial public health impact that upcoming RSV prevention strategies may provide.

Retrospectively modeling the effects of increased global vaccine sharing on the COVID-19 pandemic

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has caused considerable morbidity and mortality worldwide. The protection provided by vaccines and booster doses offered a method of mitigating severe clinical outcomes and mortality. However, by the end of 2021, the global distribution of vaccines was highly heterogeneous, with some countries gaining over 90% coverage in adults, whereas others reached less than 2%. In this study, we used an age-structured model of SARS-CoV-2 dynamics, matched to national data from 152 countries in 2021, to investigate the global impact of different potential vaccine sharing protocols that attempted to address this inequity. We quantified the effects of implemented vaccine rollout strategies on the spread of SARS-CoV-2, the subsequent global burden of disease and the emergence of novel variants. We found that greater vaccine sharing would have lowered the total global burden of disease, and any associated increases in infections in previously vaccine-rich countries could have been mitigated by reduced relaxation of non-pharmaceutical interventions. Our results reinforce the health message, pertinent to future pandemics, that vaccine distribution proportional to wealth, rather than to need, may be detrimental to all.

AN AGE-STRUCTURED MODEL FOR PERTUSSIS TRANSMISSION WITH MULTIPLE INFECTIONS STUDYING THE EFFECTS OF CHILDHOOD DTAP AND ADOLESCENT TDAPVACCINES

An age-structured deterministic model with multiple infections that accounts for decaying maternal antibody, waning infection-acquired and vaccine-induced immunity is formulated to study the transmission dynamics of pertussis and the effect of childhood DTaP and adolescent Tdap vaccines. The expression of the reproduction number [Formula: see text] is derived for the ODE model in the case of proportionate mixing. Estimated age-dependent transmission probability and empirical contact data are used in the simulation of the ODE model from which the basic reproduction number [Formula: see text] is estimated to be around 15. The combination of DTaP and Tdap vaccines fails to bring [Formula: see text] under one and thus pertussis remains endemic despite sustained high coverage of vaccination. While both DTaP and Tdap vaccines have remarkable effect on reducing the incidences of the age groups being directly vaccinated, the adolescent booster dose Tdap is also found to provide some indirect protection for infants though very limited ([Formula: see text] incidence reduction).

Dynamic behavior of an age-structured houseflies model with nonconstant fertility

Dynamic behavior of an age-structured houseflies model with nonconstant fertility