A mean-field description for the expansion kinetics of activated T cell populations.

When lymphocytes encounter their cognate antigen, they become activated and undergo a limited number of cell divisions during which they differentiate into memory or effector cells or die. While the dynamics of individual cells are often heterogeneous, the expansion kinetics at the population level are highly reproducible, suggesting a mean-field description. To generate a finite division destiny, we consider two scenarios: Cells stop dividing after a certain number of iterations or their death rate increases with each cell division. The dynamics of the combined system can be mapped to a partial differential equation, and for a suitable choice of the activation rate, we obtain simple analytical solutions for the total cell number and the mean number of divisions per cell which can well describe the signal-dependent T cell expansion kinetics from in vitro experiments. Interestingly, only the division cessation mechanism yields an expression for the division destiny that does not contradict experiments. We show that the generation-dependent decrease of the division rate in individual cells leads to a time-dependent decrease at the population level which is consistent with a "time-to-die" control mechanism for the division destiny as suggested previously. We also derive mean-field equations for the total cell number which provide a basis for implementing T cell expansion kinetics into quantitative systems pharmacology models for immuno-oncology and CAR-T cell therapies.

Assessing vaccine strategies for mpox outbreak in New York City using an age-structure model.

BACKGROUND: Since May 7 2022, mpox has been endemic in many countries which has attracted the attention of health authorities in various countries and made control decisions, in which vaccination is the mainstream strategy. However, the shortage of vaccine doses and the reduction of protective efficacy have led to unresolved issues such as vaccine allocation decisions and evaluation of transmission scale. METHODS: We developed an epidemiological model to describe the prevalence of the mpox virus in New York City and calibrated the model to match surveillance data from May 19 to November 3, 2022. Finally, we adjusted the model to simulate and compare several scenarios of non-vaccination and pre-pandemic vaccination. RESULTS: Relative to the status quo, if vaccination is not carried out, the number of new infections increases to about 385%, and the transmission time will be extended to about 350%, while if vaccinated before the epidemic, the number of new infections decreases to 94.2-96%. CONCLUSIONS: The mpox outbreak in New York City may be linked to the Pride event. However, with current vaccine coverage, there will be no more large-scale outbreaks of mpox, even if there is another similar activity. For areas with limited vaccines, priority is given to high-risk groups in the age group [34-45] years as soon as possible.

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 R 0 . When R 0 < 1 , the disease-free equilibrium is globally asymptotically stable, which means that TB epidemic will die out; When R 0 = 1 , the disease-free equilibrium is globally attractive; there exists a unique endemic equilibrium and the endemic equilibrium is globally attractive when R 0 > 1 . We estimate that the basic reproduction number R 0 = 0.5320 (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.

COVID-19 epidemic in New York City: development of an age group-specific mathematical model to predict the outcome of various vaccination strategies.

BACKGROUND: Since December 14, 2020, New York City (NYC) has started the first batch of COVID-19 vaccines. However, the shortage of vaccines is currently an inevitable problem. Therefore, optimizing the age-specific COVID-19 vaccination is an important issue that needs to be addressed as a priority. OBJECTIVE: Combined with the reported COVID-19 data in NYC, this study aimed to construct a mathematical model with five age groups to estimate the impact of age-specific vaccination on reducing the prevalence of COVID-19. METHODS: We proposed an age-structured mathematical model and estimated the unknown parameters based on the method of Markov Chain Monte Carlo (MCMC). We also calibrated our model by using three different types of reported COVID-19 data in NYC. Moreover, we evaluated the reduced cumulative number of deaths and new infections with different vaccine allocation strategies. RESULTS: Compared with the current vaccination strategy in NYC, if we gradually increased the vaccination coverage rate for only one age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 75-100 age group would be reduced the most, about 72 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0-17 age group would be reduced the most, about 21,591 fewer new infections per increased 100,000 vaccinated individuals. If we gradually increased the vaccination coverage rate for two age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 65-100 age group would be reduced the most, about 36 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0-44 age group would be reduced the most, about 17,515 fewer new infections per increased 100,000 vaccinated individuals. In addition, if we had an additional 100,000 doses of vaccine for 0-17 and 75-100 age groups as of June 1, 2021, then the allocation of 80% to the 0-17 age group and 20% to the 75-100 age group would reduce the maximum numbers of new infections and deaths simultaneously in NYC. CONCLUSIONS: The COVID-19 burden including deaths and new infections would decrease with increasing vaccination coverage rate. Priority vaccination to the elderly and adolescents would minimize both deaths and new infections.

Vaccine failure, seasonality and demographic changes associate with mumps outbreaks in Jiangsu Province, China: Age-structured mathematical modelling study.

Measles, mumps and rubella (MMR) vaccine program was introduced in Jiangsu province of China in May 2008 and has been greatly contributed to decreasing of mumps cases. However, mumps has been resurging since May 2015. A number of studies have put forward that the resurgence of mumps is due to vaccine failure. In this paper, we investigated the other reasons for the resurging of mumps, such as the changes in seasonal transmission patterns and demographic structures, by using an age-structured mathematical model. We divided the history (January 2005 to May 2019) of mumps epidemics of Jiangsu province into three different stages: No vaccine stage (January 2005 to December 2008), effectively controlled stage (January 2009 to December 2014) and resurgence stage (January 2015 to May 2019). The features of mumps epidemics in three stages are compared under different demographic structures with same physical contact rate. The mumps transmission rate was increased in summer and dropped in November in stage III compared with that in stage I. The changes in demographic structures give a good explanation why the mumps outbreaked among children around 10 years old in stage I and around 5 years old in stage III. We have a conclusion that the vaccine failure, changes in seasonality and demographic structures were associated with the mumps outbreaks in recent years in Jiangsu province, China. We give the patterns of mumps dynamics considering age, vaccine, seasonality and demographic structures, which can help health program planners to implement more preventive interventions in mumps control during the period of higher risk of infection.

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.

Evaluating Strategies For Tuberculosis to Achieve the Goals of WHO in China: A Seasonal Age-Structured Model Study.

Although great progress has been made in the prevention and mitigation of TB in the past 20 years, China is still the third largest contributor to the global burden of new TB cases, accounting for 833,000 new cases in 2019. Improved mitigation strategies, such as vaccines, diagnostics, and treatment, are needed to meet goals of WHO. Given the huge variability in the prevalence of TB across age-groups in China, the vaccination, diagnostic techniques, and treatment for different age-groups may have different effects. Moreover, the statistics data of TB cases show significant seasonal fluctuations in China. In view of the above facts, we propose a non-autonomous differential equation model with age structure and seasonal transmission rate. We derive the basic reproduction number, [Formula: see text], and prove that the unique disease-free periodic solution, [Formula: see text] is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and at least one positive periodic solution exists when [Formula: see text]. We estimate that the basic reproduction number [Formula: see text] ([Formula: see text]), which means that TB is uniformly persistent. Our results demonstrate that vaccinating susceptible individuals whose ages are over 65 and between 20 and 24 is much more effective in reducing the prevalence of TB, and each of the improved vaccination strategy, diagnostic strategy, and treatment strategy leads to substantial reductions in the prevalence of TB per 100,000 individuals compared with current approaches, and the combination of the three strategies is more effective. Scenario A (i.e., coverage rate [Formula: see text], diagnosis rate [Formula: see text], relapse rate [Formula: see text]) is the best and can reduce the prevalence of TB per 100,000 individuals by [Formula: see text] and [Formula: see text] in 2035 and 2050, respectively. Although the improved strategies will significantly reduce the incidence rate of TB, it is challenging to achieve the goal of WHO in 2050. Our findings can provide guidance for public health authorities in projecting effective mitigation strategies of TB.

Combating COVID-19 crisis and predicting the second wave in Europe: an Age-structured modeling.

We employ an age-structured susceptible-infected-quarantined-recovered model to simulate the progression of COVID-19 in France, Spain, and Germany. In the absence of a vaccine or conventional treatment, non-pharmaceutical interventions become more valuable, so our model takes into account the efficacy of official social distancing and lockdown measures. Using data from February to July 2020, we make useful predictions for the upcoming months, and further simulate the effect of lifting the lockdown at a later stage. A control model is also proposed and conditions for optimality are also obtained using optimal control theory. Motivated by the recent surge in cases in France and Spain, we also examine the possibility of a second wave of the pandemic. We conclude that further measures need to be taken in these two countries, while Germany is on its way to mitigating the disease.

Evaluating the independent influence of sexual transmission on HBV infection in China: a modeling study.

BACKGROUND: The long-term impact of sexual transmission on the hepatitis B virus (HBV) infection in China remains unclear. This study aims to estimate the independent influence of sexual transmission on HBV infection. METHODS: Based on the natural history of HBV infection and three national serosurvey data of hepatitis B in China, we developed an age- and sex-specific discrete model to describe the transmission dynamics of HBV. The initial conditions of the model were determined according to the age- and sex-specific national serosurvey data in 1992. Based on the national survey data of hepatitis B in 1992 and 2006, by using the Markov Chain Monte Carlo (MCMC) method, we estimated the age- and sex-specific seroclearance rates of hepatitis B surface antigen (HBsAg) and the horizontal transmission rates as well as their 95% confidence intervals (CI). Then we used the age- and sex-specific national serosurvey data of hepatitis B in 2014 to test the accuracy of our model-based estimation. Finally, we evaluated the independent impact of sexual transmission on HBV infection and discussed the long-term effect of promotion of condom use in China. RESULTS: We estimated that the annual rates of HBsAg seroclearance for males and females aged 1-59 years were respectively 1.04% (95% CI, 0.49-1.59%) and 1.92% (95% CI, 1.11-2.73%). Due to sexual transmission, in 2014, the total number of chronic HBV infections in people aged 0-100 years increased 292,581, of which males increased 189,200 and females increased 103,381. In 2006, the acute HBV infections due to sexual transmission accounted for 24.76% (male: 31.33%, female: 17.94%) and in 2014, which accounted for 34.59% (male: 42.93%, female: 25.73%). However, if the condom usage rate was increased by 10% annually starting in 2019, then compared with current practice, the total number of acute HBV infections from 2019 to 2035 would be reduced by 16.68% (male: 21.49%, female: 11.93%). The HBsAg prevalence in people aged 1-59 years in 2035 would be reduced to 2.01% (male: 2.40%, female: 1.58%). CONCLUSIONS: Sexual transmission has become the predominant route of acute HBV infection in China, especially for men. The promotion of condom use plays a significant role in reducing the cases of acute HBV infection.

Optimal harvesting in the presence of predation: An age-structured modelling approach.

Predation of wildlife and livestock by large carnivores takes place within many ecological and institutional settings. In this paper, moose predation by wolves is studied within a Norwegian institutional setting where the landowners obtain the moose harvesting value and where the wolf population is strictly controlled by the wildlife authorities. An age-structured model consisting of four categories of the moose population (calves, yearlings and adult females and males) is formulated, and both maximum yield (MY) and maximum economic yield (MEY) harvesting are studied. We find that the direct effect of higher predation pressure on an age-sex category works in the direction of higher harvesting pressure of that group. However, this direct effect is accompanied by indirect effects working through the stock abundance of all age-sex groups, and the net effect is ambiguous. In the numerical analysis, it is shown that harvest of the adult categories typically will be the optimal strategy, irrespective of the fact that calves are the main target of the wolves.

A game-theoretical analysis of poliomyelitis vaccination.

Poliomyelitis is a worldwide disease that has nearly been eradicated thanks to the Global Polio Eradication Initiative. Nevertheless, the disease is currently still endemic in three countries. In this paper, we incorporate the vaccination in a two age-class model of polio dynamics. Our main objective is to see whether mandatory vaccination policy is needed or if polio could be almost eradicated by a voluntary vaccination. We perform game theoretical analysis and compare the herd immunity vaccination levels with the Nash equilibrium vaccination levels. We show that the gap between two vaccination levels is too large. We conclude that the mandatory vaccination policy is therefore needed to achieve a complete eradication.

The Optimal Age of Vaccination Against Dengue with an Age-Dependent Biting Rate with Application to Brazil.

In this paper we introduce a single serotype transmission model, including an age-dependent mosquito biting rate, to find the optimal vaccination age against dengue in Brazil with Dengvaxia. The optimal vaccination age and minimal lifetime expected risk of hospitalisation are found by adapting a method due to Hethcote (Math Biosci 89:29-52). Any number and combination of the four dengue serotypes DENv1-4 is considered. Successful vaccination against a serotype corresponds to a silent infection. The effects of antibody-dependent enhancement (ADE) and permanent cross-immunity after two heterologous infections are studied. ADE is assumed to imply risk-free primary infections, while permanent cross-immunity implies risk-free tertiary and quaternary infections. Data from trials of Dengvaxia indicate vaccine efficacy to be age and serostatus dependent and vaccination of seronegative individuals to induce an increased risk of hospitalisation. Some of the scenarios are therefore reconsidered taking these findings into account. The optimal vaccination age is compared to that achievable under the current age restriction of the vaccine. If vaccination is not considered to induce risk, optimal vaccination ages are very low. The assumption of ADE generally leads to a higher optimal vaccination age in this case. For a single serotype vaccination is not recommended in the case of ADE. Permanent cross-immunity results in a slightly lower optimal vaccination age. If vaccination induces a risk, the optimal vaccination ages are much higher, particularly for permanent cross-immunity. ADE has no effect on the optimal vaccination age when permanent cross-immunity is considered; otherwise, it leads to a slight increase in optimal vaccination age.

Prioritization of vaccine strategy using an age-dependent mathematical model for 2009 A/H1N1 influenza in the Republic of Korea.

We developed a mathematical model of the 2009 A/H1N1 influenza epidemic in the Republic of Korea by considering five age groups and suggested the best way to prioritize an age-dependent vaccination strategy for mitigating the epidemic. An age-structured SEIAR influenza model was constructed based on the laboratory confirmed data obtained from the Korea Centers for Disease Control and Prevention (KCDC). The estimated transmission matrix captured one of the main characteristics of the 2009 A/H1N1 influenza, the transmission rate of which is high among young people, unlike that of seasonal influenza. We investigated the impact of age-dependent vaccination priority on the transmission dynamics of the 2009 A/H1N1 influenza and evaluated the Korean government vaccination policy when the vaccination started being administered 90 days (or 120 days) after the onset of the outbreak. We found that the government's age priority vaccination policy (Group 2, Group 1, Group 5, Group 4, and Group 3 in order) was a good strategy for reducing 62.06% of the cumulative cases when the vaccination was applied 90 days after the onset of the outbreak, while the proposed model's best suggestion (Group 2, Group 1, Group 3, Group 4, and Group 5 in order) showed 64.52% reduction. Furthermore, we studied the region-specific vaccination policy. For instance, the best age-priority of vaccination in Gwangwon province showed a different order (Group 3, Group 1, Group 2, Group 4, and Group 5 in order) and it reduced the incidence by 58.1%, which is 5.54% higher than that of the 2009 Korean government policy.

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays.

Scratch assays are in vitro methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. Typically, scratch assays are modelled by reaction diffusion equations depicting cell migration by Fickian diffusion and proliferation by a logistic term. In a recent paper (Jin et al. in Bull Math Biol 79(5):1028-1050, 2017), the authors observed experimentally that during the early stage of the recolonisation process, there is a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. The authors did not identify the precise mechanism that causes the disturbance phase but showed that ignoring it can lead to incorrect parameter estimates. The aim of this work is to show that a nonlinear age-structured population model can account for the two phases of proliferation in scratch assays. The model consists of an age-structured cell cycle model of a cell population, coupled with an ordinary differential equation describing the resource concentration dynamics in the substrate. The model assumes a resource-dependent cell cycle threshold age, above which cells are able to proliferate. By studying the dynamics of the full system in terms of the subpopulations of cells that can proliferate and the ones that can not, we are able to find conditions under which the model captures the two-phase behaviour. Through numerical simulations, we are able to show that the interplay between the resource concentration in the substrate and the cell subpopulations dynamics can explain the biphasic dynamics.

Fine-scale population dynamics in a marine fish species inferred from dynamic state-space models.

Identifying the spatial scale of population structuring is critical for the conservation of natural populations and for drawing accurate ecological inferences. However, population studies often use spatially aggregated data to draw inferences about population trends and drivers, potentially masking ecologically relevant population sub-structure and dynamics. The goals of this study were to investigate how population dynamics models with and without spatial structure affect inferences on population trends and the identification of intrinsic drivers of population dynamics (e.g. density dependence). Specifically, we developed dynamic, age-structured, state-space models to test different hypotheses regarding the spatial structure of a population complex of coastal Atlantic cod (Gadus morhua). Data were from a 93-year survey of juvenile (age 0 and 1) cod sampled along >200 km of the Norwegian Skagerrak coast. We compared two models: one which assumes all sampled cod belong to one larger population, and a second which assumes that each fjord contains a unique population with locally determined dynamics. Using the best supported model, we then reconstructed the historical spatial and temporal dynamics of Skagerrak coastal cod. Cross-validation showed that the spatially structured model with local dynamics had better predictive ability. Furthermore, posterior predictive checks showed that a model which assumes one homogeneous population failed to capture the spatial correlation pattern present in the survey data. The spatially structured model indicated that population trends differed markedly among fjords, as did estimates of population parameters including density-dependent survival. Recent biomass was estimated to be at a near-record low all along the coast, but the finer scale model indicated that the decline occurred at different times in different regions. Warm temperatures were associated with poor recruitment, but local changes in habitat and fishing pressure may have played a role in driving local dynamics. More generally, we demonstrated how state-space models can be used to test evidence for population spatial structure based on survey time-series data. Our study shows the importance of considering spatially structured dynamics, as the inferences from such an approach can lead to a different ecological understanding of the drivers of population declines, and fundamentally different management actions to restore populations.

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise.

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability is strikingly similar.

Increased transmissibility explains the third wave of infection by the 2009 H1N1 pandemic virus in England.

In the 2009 H1N1 pandemic, the United Kingdom experienced two waves of infection, the first in the late spring and the second in the autumn. Given the low level of susceptibility to the pandemic virus expected to be remaining in the population after the second wave, it was a surprise that a substantial third epidemic occurred in the UK population between November 2010 and February 2011, despite no evidence for any significant antigenic evolution of the pandemic virus. Here, we use a mathematical model of influenza transmission embedded within a Bayesian synthesis inferential framework to jointly analyze syndromic, virological, and serological surveillance data collected in England in 2009-2011 and thereby assess epidemiological mechanisms which might have generated the third wave. We find that substantially increased transmissibility of the H1N1pdm09 virus is required to reproduce the third wave, suggesting that the virus evolved and increased fitness in the human host by the end of 2010, or that the very cold weather experienced in the United Kingdom at that time enhanced transmission rates. We also find some evidence that the preexisting heterologous immunity which reduced attack rates in adults during 2009 had substantially decayed by the winter of 2010, thus increasing the susceptibility of the adult population to infection. Finally, our analysis suggests that a pandemic vaccination campaign targeting adults and school-age children could have mitigated or prevented the third wave even at moderate levels of coverage.

Impact of immunity loss on the optimal vaccination strategy for an age-structured epidemiological model.

The pursuit of effective vaccination strategies against COVID-19 remains a critical endeavour in global public health, particularly amidst challenges posed by immunity loss and evolving epidemiological dynamics. This study investigated optimal vaccination strategies by considering age structure, immunity dynamics, and varying maximal vaccination rates. To this end, we formulated an SEIR model stratified into $ n $ age classes, with the vaccination rate as an age-dependent control variable in an optimal control problem. We developed an objective function aimed at minimising critical infections while optimising vaccination efforts and then conducted rigorous mathematical analyses to ensure the existence and characterization of the optimal control. Using data from three countries with diverse age distributions, in expansive, constrictive, and stationary pyramids, we performed numerical simulations to evaluate the optimal age-dependent vaccination strategy, number of critical infections, and vaccination frequency. Our findings highlight the significant influence of maximal vaccination rates on shaping optimal vaccination strategies. Under constant maximal vaccination rates, prioritising age groups based on population demographics proves effective, with higher rates resulting in fewer critically infected individuals across all age distributions. Conversely, adopting age-dependent maximal vaccination rates, akin to the WHO strategy, may not always lead to the lowest critical infection peaks but offers a viable alternative in resource-constrained settings.

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.

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.