Age-structured Model Research Articles

New developments in the analysis of catch time series as the basis for fish stock assessments: The CMSY++ method

Following an introduction to the nature of fisheries catches and their information content, a new development of CMSY, a data-limited stock assessment method for fishes and invertebrates, is presented. This new version, CMSY++, overcomes several of the deficiencies of CMSY, which itself improved upon the “Catch-MSY” method published by S. Martell and R. Froese in 2013. The catch-only application of CMSY++ uses a Bayesian implementation of a modified Schaefer model, which also allows the fitting of abundance indices should such information be available. In the absence of historical catch time series and abundance indices, CMSY++ depends strongly on the provision of appropriate and informative priors for plausible ranges of initial and final stock depletion. An Artificial Neural Network (ANN) now assists in selecting objective priors for relative stock size based on patterns in 400 catch time series used for training. Regarding the cross-validation of the ANN predictions, of the 400 real stocks used in the training of ANN, 94% of final relative biomass (B/k) Bayesian (BSM) estimates were within the approximate 95% confidence limits of the respective CMSY++ estimate. Also, the equilibrium catch-biomass relations of the modified Schaefer model are compared with those of alternative surplus-production and age-structured models, suggesting that the latter two can be strongly biased towards underestimating the biomass required to sustain catches at low abundance. Numerous independent applications demonstrate how CMSY++ can incorporate, in addition to the required catch time series, both abundance data and a wide variety of ancillary information. We stress, however, the caveats and pitfalls of naively using the built-in prior options, which should instead be evaluated case-by-case and ideally be replaced by independent prior knowledge.

Evaluating the cost-effectiveness of HPV vaccination for adolescent girls in Japan: A comparison of 2-valent, 4-valent, and 9-valent HPV vaccines with consideration of cross-protection

ObjectiveIn April 2023, the Japanese Health Ministry panel approved the inclusion of the 9-valent human papillomavirus (9vHPV) vaccine in the National Immunization Program, alongside the 2-valent (2vHPV) and 4-valent HPV (4vHPV) vaccines. In response to this, we evaluated the cost-effectiveness of these three vaccines for routine immunization of girls aged 12–16 in Japan, considering the cross-protection of 2vHPV and 4vHPV vaccines. MethodsWe constructed an age-structured mathematical model for HPV transmission, aiming to quantify the economic and epidemiological effects of various HPV vaccination strategies over a 70-year period in Japan. We determined incremental costs and quality-adjusted life years (QALYs) for each strategy, applying a 3% annual discount. Univariate and probabilistic sensitivity analyses were conducted to assess the uncertainty of our model results, with all evaluations done in 2023. ResultsOur projections indicate that the HPV vaccination program in Japan will significantly reduce the incidence of HPV-related diseases. All HPV vaccination strategies, using the 2vHPV, 4vHPV, and 9vHPV vaccines, were found to be cost-effective compared to no vaccination, with incremental cost-effectiveness ratios of ¥971,447/QALY, ¥1,237,297/QALY, and ¥742,084/QALY, respectively. Direct comparisons between vaccines demonstrated that the 9vHPV vaccination was more cost-effective than the 2vHPV vaccination, whereas 4vHPV vaccination was dominated by 2vHPV vaccination. ConclusionsOur study validates the cost-effectiveness of implementing the 9vHPV vaccine as the primary option over the 2vHPV or 4vHPV vaccine for girls in Japan. These findings underscore the need to improve the acceptance rate and coverage of HPV vaccinations in the country.

Dynamics of hand, foot and mouth disease in children under 15 years old: A case study of Malaysia using age-structured modelling approach

Hand, foot, and mouth disease (HFMD) is a viral infection that primarily affects children. The disease is characterized by fever, sores in the mouth, and a rash on the hands, feet, and buttocks. In this case study, we analyze the dynamics of HFMD in children under 15 years old in Malaysia using an age-structured modeling approach. First we prove backward bifurcation for a baseline model which is then extended to an age-structured model. We used data on the incidence of HFMD in Malaysia from 2021 to 2022 to calibrate the model parameters and simulate the disease dynamics. Sensitivity analysis is done by Latin hypercube sampling - partial rank correlation coefficient (LHS/PRCC) method. Simulation is done and the impact of imperfect vaccine and quarantine is explored. Our results show that the dynamics of the disease is mostly driven by children under 5 years old. The model also predicts that vaccination could significantly reduce the incidence of HFMD in Malaysia. Vaccination is most effective when targeted at young children, who are at the highest risk of disease as this will lead to drastic decrease in the incidence of HFMD in all age groups. Our simulations show that quarantining of infected children until they fully recover will reduce the transmission of HFMD, but this strategy needs to be sustained for a sufficient duration to have a significant impact. The result of this paper can inform the development of policies for controlling the spread of HFMD and other infectious diseases in Malaysia and other similar settings.

Dynamical analysis of an age-structured cholera transmission model on complex networks

Cholera is a water- and food-borne infectious disease caused by the bacterium Vibrio cholerae. In this paper, we present a novel modeling framework to investigate the effect of infection age on cholera transmission in a heterogeneous population. Our model is constructed on a system with infection age on complex networks, including both direct and indirect transmission routes and demographics. The basic reproduction number R0 is derived as the spectral radius of the next generation operator, and it is verified that R0 is a sharp threshold that determines whether cholera becomes extinct or not. Numerical simulations are performed to confirm the theoretical results. Furthermore, the sensitivity analysis of the basic reproduction number to the parameters suggests that the implementation of effective drug treatment for infected individuals and the timely removal of pathogens from contaminated water are beneficial to control the spread of cholera.

Co-management of a high-value species with territorial use rights for fisheries: a spatial bioeconomic approach with environmental variability

Abalone is a high-value resource that is an important export market fishery of Mexico that is managed through territorial use rights for fisheries allocated to a coastal community. A specific age-structured spatial bioeconomic model was applied to this fishery to undertake stock recovery to target levels. The model incorporates uncertainty in the parameter k of a von Bertalanffy growth function with environmental variability. The risk of falling below and exceeding the target and bioeconomic limit reference points of the population with alternative fisheries management strategies was studied using a Monte Carlo analysis. The management strategy evaluation showed that Emin (minimum effort) and EmaxNPV (resource rent maximization effort) generated higher biomass levels and higher present value of resource rent than Emsy (effort in maximum sustainable yield) at the end of the simulation period, regardless of the bioeconomic reference points and assuming a reduction in fishing effort. Emin and EmaxNPV increased and maximized the present value of resource rent generated by the species while avoiding its overexploitation. The social consequences of the management strategies were considered with the participation of fishers of this co-managed fishery.

DECIPHERING DYNAMICS OF COVID-19 OUTBREAK IN INDIA: AN AGE-STRUCTURED MODEL

The dynamics of infectious disease transmission depends on social contact patterns and the precautions people take to minimize disease transmission. The social contact pattern varies depending on the community at large age distribution at work, school, and recreation. Consequently, knowing the age-specific prevalence and incidence of infectious diseases is critical for predicting future disease burden and the efficacy of interventions like vaccination. In this study, we use an SEIR age-structured multi-group epidemic model to understand how social contact affects disease control. We construct location-specific social contact matrices to observe that how social mixing affects disease spread. For mathematical analysis, we compute the basic reproduction number [Formula: see text] and exhibit the global behavior of the system in terms of [Formula: see text]. We also estimate the transmission rate using the empirical data of COVID-19 for India from 1 September 2020, to 31 December 2020. We simulate the lifting of non-pharmaceutical interventions by allowing people to return to work in phases and investigate its impact. Our findings imply that raising awareness in symptomatic infected individuals aged 20–49 years can help in reducing the number of infected individuals. When some schools are partially open, awareness in symptomatic infected individuals in school-age groups also plays a significant role in reducing disease cases. The simulation results also suggest that limiting contact at school and other gathering places could significantly lower the number of instances. Using the least square approach, we show that the time-dependent transmission rate is more realistic than the constant spread rate for COVID-19 in India. To reduce the COVID-19 burden, we obtain that gradually loosening control measures could flatten and lower other peaks. Our findings may help health policymakers to decide on timely age-based vaccination distribution strategies and control measures.

The robustness of our assumptions about recruitment: A re-examination of marine recruitment dynamics with additional data and novel methods

Recruitment is the number of young fish entering a population and is an essential process in age-structured stock assessment models. Many of the models on which stock assessments are based assume some level of influence of spawning biomass on recruitment, and estimation of this functional relationship has been a focus of substantial research. However, recruitment is also influenced by environmental fluctuations that induce autocorrelated patterns, trends, and shifts in deviations from the stock-recruitment relationship. Consequently, previous meta-analyses of stock-recruitment relationships have had trouble calibrating the relationship. We revisited the findings of Szuwalski et al. (2015) to determine if their results are robust to the addition of data to the RAM Legacy Stock Assessment database and choice of analysis method (the PELT algorithm, MARSS models, and Bayesian change point detection). Since the publication of Szuwalski et al. (2015), the number of stocks in the database has doubled. We determined the primary influence of spawning biomass on recruitment and examined the recruitment time series for regime shifts for 432 stocks. Our results indicated that 57% of stocks did not have a significant correlation between spawning biomass and recruitment over the observed biomasses. Environmental conditions played a larger role in recruitment variation than spawning biomass. The presence, location, and number of regime shifts in recruitment time series was highly dependent on the detection method, with Bayesian change point detection identifying the fewest regime shifts. Despite the sensitivity to the detection method, 46% of stocks without a significant correlation between spawning biomass and recruitment are estimated to have experienced at least one regime shift as determined by the PELT algorithm Our analyses suggest that effective methods for modeling and forecasting large variations in recruitment over time are needed, particularly given that climate change is predicted to impact the frequency and magnitude of regime shifts.

Cost-effectiveness analysis of COVID-19 variants effects in an age-structured model

This study analyzes the impact of COVID-19 variants on cost-effectiveness across age groups, considering vaccination efforts and nonpharmaceutical interventions in Republic of Korea. We aim to assess the costs needed to reduce COVID-19 cases and deaths using age-structured model. The proposed age-structured model analyzes COVID-19 transmission dynamics, evaluates vaccination effectiveness, and assesses the impact of the Delta and Omicron variants. The model is fitted using data from the Republic of Korea between February 2021 and November 2022. The cost-effectiveness of interventions, medical costs, and the cost of death for different age groups are evaluated through analysis. The impact of different variants on cases and deaths is also analyzed, with the Omicron variant increasing transmission rates and decreasing case-fatality rates compared to the Delta variant. The cost of interventions and deaths is higher for older age groups during both outbreaks, with the Omicron outbreak resulting in a higher overall cost due to increased medical costs and interventions. This analysis shows that the daily cost per person for both the Delta and Omicron variants falls within a similar range of approximately $10–$35. This highlights the importance of conducting cost-effect analyses when evaluating the impact of COVID-19 variants.

Unravelling the web of tuberculosis: Mathematical models to decode and defeat tuberculosis transmission complexity

In the transmission of infectious illnesses like tuberculosis, mathematical models are crucial in public health. The fundamental paradigm is compartmental modelling, which classifies people into categories such as susceptible, latent, active, and recovered. Extensions and variations in this model can be utilized to capture intricate details. To research TB transmission dynamics, structural models including age-structured, agent-based, stochastic, SEIR, spatial, drug-resistant, vaccination, contact tracking, and treatment models are employed. Populations are divided into age groups by age-structured models, intricate interactions are shown by agent-based models, disease outbreaks are simulated by stochastic models, social networks are considered by SEIR models, and treatment success rates are considered by treatment models. Real-world mathematical simulations of TB transmission in public health settings offer useful tools for comprehending TB dynamics, making decisions, allocating resources, and assisting in the reduction and eradication of tuberculosis.

Threshold dynamics of an age-structured vaccinated epidemic model with both direct and indirect routes of infections

Age-structured epidemic models play a crucial role in the study of epidemiological modeling. Motivated by this, in this article, we propose an epidemic model with age since infection and vaccination age of individuals, a coupled system of PDE and integro-differential equations (IDE). Here, two contagious routes, (a) direct human-to-human contact and (b) indirect environmentally contaminated surfaces or objects are considered. First, we establish the well-posedness of the model, followed by the basic reproduction number (R0) and the role of the threshold value of R0 in the asymptotic profile of the solution semi-flow is established. We observe the global stability of the disease-free steady state for R0<1, the uniform persistence of the disease and the existence of the endemic steady state for R0>1. This endemic steady state is also globally asymptotically stable for R0>1. We have further analyzed the influence of vaccination age and age since infection in the threshold parameter R0. Our analysis shows that the threshold parameter R0 does not depend explicitly on vaccination age, but it strictly decreases with the natural depletion rate of the contaminated environment. Finally, the model is discretized using the finite difference method to illustrate our theoretical results numerically.

Equitable bivalent booster allocation strategies against emerging SARS-CoV-2 variants in US cities with large Hispanic communities: The case of El Paso County, Texas.

COVID-19 is a disease that disproportionately impacts the Hispanic population, due to the prevalence of certain risk factors and the high number of essential workers in this community. In this work, we analyze the vaccination strategies that would minimize the COVID-19 health disparities in El Paso County, TX, in the context of the emergence of a new highly transmissible and immune-escaping SARS-CoV-2 variant. We stratify an age-structure stochastic SEIR model that tracks the evolution of immunity derived from infections and vaccination according to Hispanic vs non-Hispanic ethnicity and parameterize it to the demographic, health and immunization data of El Paso County, TX. After fitting the model, the results show that increasing vaccination with bivalent boosters by five-fold in anticipation of highly transmissible and immune escaping variants would decrease the cumulative hospital admissions and mortality from Mar 1, 2023, to Dec 31, 2023, by 62.72% and 61.41%, respectively. Further, our projections reveal that the disproportionate impact on the Hispanic community would be eliminated if approximately half of the doses that are given to the non-Hispanic group according to the equal distribution, would be re-allocated to the Hispanic population. Our findings can guide public health officials in US cities with large Hispanic communities and help them design vaccination strategies that minimize COVID-19 health disparities caused by emerging variants using specific vaccination strategies.

Global asymptotic stability in a pseudorabies virus model with age structure.

Pseudorabies is a highly contagious disease caused by pseudorabies virus (PRV) or suid herpesvirus 1 (SuHV1), causing significant economic losses to the swine industry in countries where the disease exists. In this paper, we formulate an age structure model of pseudorabies virus that takes into account disease-related mortality and vertical transmission. We find a threshold to determine the stability and existence of the disease. We show that there is always a globally asymptotically stable boundary equilibrium if and only if , which means that the disease always exists in piglets and will die out in adult pigs. When , the boundary equilibrium is unstable and there exists a unique disease-endemic equilibrium, which is globally asymptotically stable. We give detailed proofs of our theoretical results and numerical examples. Brief concluding remarks are also provided.

Mathematical analysis of a multiscale hepatitis C virus infection model with two viral strains

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

Asymptotic behavior of the basic reproduction number in an age-structured SIS epidemic patch model.

In this paper we consider an age-structured SIS epidemic patch model. We define the principal eigenvalue [Formula: see text], basic reproduction number [Formula: see text] and analyze the effects of the diffusion rate d on [Formula: see text] and [Formula: see text]. More precisely, we investigate their asymptotic behavior for small and large diffusion rates. Finally we study the global behavior of this age-structured SIS epidemic patch model.

Global Dynamics of an Age-Structured Tuberculosis Model with Vaccine Failure and Nonlinear Infection Force

Global Dynamics of an Age-Structured Tuberculosis Model with Vaccine Failure and Nonlinear Infection Force

A model-based strategy for the COVID-19 vaccine roll-out in the Philippines

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered: young (0–19 years), adult (20–64 years), and elderly (65+ years). The transmission rate and reporting rate are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.

Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine

Based on the spread of COVID-19, in the present paper, an imperfectly vaccinated SVEIR model for latent age is proposed. At first, the equilibrium points and the basic reproduction number of the model are calculated. Then, we discuss the asymptotic smoothness and uniform persistence of the semiflow generated by the solutions of the system and the existence of an attractor. Moreover, LaSalle’s invariance principle and Volterra type Lyapunov functions are used to prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number Rρ is less than one, the disease will gradually disappear. However, if the number is greater than one, the disease will become endemic and persist. In addition, numerical simulations are also carried out to verify the result. Finally, suggestions are made on the measures to control the ongoing transmission of COVID-19.

Greenland halibut stock state and fishery magement in the Barents Sea

The subject of this article is an assessment of reference points and the state of the black halibut stock in the Barents Sea. Despite the abundance of information accumulated over the years of fishing and research, the uncertainty of the dynamics of the stock remains quite high. The article describes and analyzes all currently known sources of information about the state of the stock –data from surveys, fishing statistics and the age structure of catches. Several types of models are being built – production models and age-structured model. The MSY value at the level of 28–32 thousand tons were obtained as a result of applying three different approaches to stock modeling: production models, combining cohort and production models and constructing a yield-recruit curve based on cohort models data. Despite the much greater uncertainty in the estimates of biomass, the current fishing intensity can be considered close to optimal based on the estimates obtained.

Epidemic dynamics with time-varying transmission risk reveal the role of disease stage-dependent infectiousness

A key characteristic of acute communicable diseases is the infectiousness that varies over time as the infection dynamics evolve within a host, which influences the risk of transmission in different stages of the disease. Despite the evidence of time-varying transmission risk, most dynamic models of epidemics assume a constant transmission rate during the infectious period. Recent work has shown the difference in epidemic dynamics when this assumption is relaxed and different transmission rates are used by discretizing the infectious period into multiple sub-periods. Here, we develop an age-structured model to integrate a continuous time-varying transmission risk, based on an established correlation between the viral dynamics and infectiousness profile. Taking into account the natural history and parameter estimates of COVID-19 caused by the original strain of SARS-CoV-2, we demonstrate the difference in temporal epidemic dynamics when a continuous time-varying transmission probability is used as compared to multiple constant transmission probabilities. Our results show a significant difference between the incidence curves in terms of the magnitude and peak time, even when the reproduction number and total number of infections are the same for continuous and discrete transmission probabilities. Finally, we demonstrate the spurious outcome of preventing an epidemic through the isolation of infectious individuals when constant transmission probabilities are used, highlighting the importance of integrating a continuous time-dependent transmission parameter in dynamic models. These findings suggest a more cautious interpretation of model outcomes, especially those that are intended to evaluate the effectiveness of interventions and inform policy decisions for disease mitigation strategies.

Stationary status of discrete and continuous age-structured population models

From Leonhard Euler to Alfred Lotka and in recent years understanding the stationary process of the human population has been of central interest to scientists. Population reproductive measure NRR (net reproductive rate) has been widely associated with measuring the status of population stationarity and it is also included as one of the measures in the millennium development goals. This article argues how the partition theorem-based approach provides more up-to-date and timely measures to find the status of the population stationarity of a country better than the NRR-based approach. We question the timeliness of the value of NRR in deciding the stationary process of the country. We prove associated theorems on discrete and continuous age distributions and derive measurable functional properties. The partitioning metric captures the underlying age structure dynamic of populations at or near stationarity. As the population growth rates for an ever-increasing number of countries trend towards replacement levels and below, new demographic concepts and metrics are needed to better characterize this emerging global demography.