Coevolution of Age-Structured Tolerance and Virulence.

Hosts can evolve a variety of defences against parasitism, including resistance (which prevents or reduces the spread of infection) and tolerance (which protects against virulence). Some organisms have evolved different levels of tolerance at different life-stages, which is likely to be the result of coevolution with pathogens, and yet it is currently unclear how coevolution drives patterns of age-specific tolerance. Here, we use a model of tolerance-virulence coevolution to investigate how age structure influences coevolutionary dynamics. Specifically, we explore how coevolution unfolds when tolerance and virulence (disease-induced mortality) are age-specific compared to when these traits are uniform across the host lifespan. We find that coevolutionary cycling is relatively common when host tolerance is age-specific, but cycling does not occur when tolerance is the same across all ages. We also find that age-structured tolerance can lead to selection for higher virulence in shorter-lived than in longer-lived hosts, whereas non-age-structured tolerance always leads virulence to increase with host lifespan. Our findings therefore suggest that age structure can have substantial qualitative impacts on host-pathogen coevolution.

Global stability and optimal control of an age-structured SVEIR epidemic model with waning immunity and relapses.

The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse. Next, the asymptotic smoothness, the uniform persistence and the existence of interior global attractor of the solution semi-flow generated by the system are given. We define the basic reproduction number R 0 and prove the existence of the equilibria of the model. And we study the global asymptotic stability of the equilibria. Then the parameters of the model are estimated using tuberculosis data in China. The sensitivity analysis of R 0 is derived by the Partial Rank Correlation Coefficient method. These main theoretical results are applied to analyze and predict the trend of tuberculosis prevalence in China. Finally, the optimal control problem of the model is discussed. We choose to take strengthening treatment and controlling relapse as the control parameters. The necessary condition for optimal control is established.

Evaluation of age-structured vaccination strategies for curbing the disease spread.

Age structure is one of the crucial factors in characterizing the heterogeneous epidemic transmission. Vaccination is regarded as an effective control measure for prevention and control epidemics. Due to the shortage of vaccine capacity during the outbreak of epidemics, how to design vaccination policy has become an urgent issue in suppressing the disease transmission. In this paper, we make an effort to propose an age-structured SVEIHR model with the disease-caused death to take account of dynamics of age-related vaccination policy for better understanding disease spread and control. We present an explicit expression of the basic reproduction number R 0 , which determines whether or not the disease persists, and then establish the existence and stability of endemic equilibria under certain conditions. Numerical simulations are illustrated to show that the age-related vaccination policy has a tremendous influence on curbing the disease transmission. Especially, vaccination of people over 65 is better than for people aged 21-65 in terms of rapid eradication of the disease in Italy.

Livestock turnover and dynamic livestock carrying capacity are crucial factors for alpine grassland management: The Qinghai-Tibetan plateau as a case study.

Alpine grasslands are distributed widely on high-elevated ranges and plateaus from the wet tropics to polar regions, accounting for approximately 3% of the world's land area. The Qinghai-Tibetan Plateau (QTP) is the highest and largest plateau in the world, and approximately 60% of the plateau consists of alpine grassland, which is used mainly for grazing animals. Livestock structure was determined in Guinan (GN), Yushu (YS) and Maqu counties (MQ) on the QTP by interviewing 235 local pastoralists. Based on data collected from GN, the livestock carrying capacity was calculated using herbage dry matter biomass intake (LCCm) by the livestock, and the metabolizable energy yield (LCCe) and digestible crude protein (LCCp) available in pasture. The pasture area per household differed among the regions of the QTP, which was the main reason for the difference in livestock stocking rate. The householders raised the appropriate proportion of breeding females and young yaks and sheep in GN and MQ, but not in YS, to maintain a constant turnover. Most pasture in YS was used at the community level, especially in summer. The calculated carrying capacities based on metabolizable energy yield (LCCe) of the pasture and dry matter biomass (LCCm) were similar in most months except for August, when the value of LCCe was higher than LCCm. Based on the digestible protein of the pasture, the calculated livestock carrying capacity overestimated the actual carrying capacity during the herbage growing season from May to September. Appropriate practices should be taken in different regions of QTP, such as providing supplementary feed, especially protein, during the forage non-growing season. Livestock carrying capacity should be adjusted dynamically, and calculated by a number of parameters. The stocking rate should be controlled to optimize livestock production and curb or minimize grassland degradation to generate a sustainable system. This study examined the grasslands and LCC on the QTP, but the results could be applied to grasslands worldwide.

Individual and Population Age Impact Social Behavior and Network Structure in a Long-Lived Insect.

AbstractSocial behaviors vary among individuals, and social networks vary among groups. Understanding the causes of such variation is important for predicting or altering ecological processes such as infectious disease outbreaks. Here, we ask whether age contributes to variation in social behavior at multiple levels of organization: within individuals over time, among individuals of different ages, among local social environments, and among populations. We used experimental manipulations of captive populations and a longitudinal dataset to test whether social behavior is associated with age across these levels in a long-lived insect, the forked fungus beetle (Bolitotherus cornutus). In cross-sectional analyses, we found that older beetles were less connected in their social networks. Longitudinal data confirmed that this effect was due in part to changes in behavior over time; beetles became less social over 2 years, possibly because of increased social selectivity or reproductive investment. Beetles of different ages also occupied different local social neighborhoods. The effects of age on behavior scaled up: populations of older individuals had fewer interactions, fewer but more variable relationships, longer network path lengths, and lower clustering than populations of young individuals. Age therefore impacted not only individual sociality but also the network structures that mediate critical population processes.

Null Models for the Opportunity for Selection.

AbstractCrow's "opportunity for selection" (I=variance in relative fitness) is an important albeit controversial eco-evolutionary concept, particularly regarding the most appropriate null model(s). Here, we treat this topic in a comprehensive way by considering opportunities for both fertility selection (If) and viability selection (Im) for discrete generations, both seasonal and lifetime reproductive success in age-structured species, and experimental designs that include either a full or partial life cycle, with complete enumeration or random subsampling. For each scenario, a null model that includes random demographic stochasticity can be constructed that follows Crow's initial formulation that I=If+Im. The two components of I are qualitatively different. Whereas an adjusted If (ΔIf) can be computed that accounts for random demographic stochasticity in offspring number, Im cannot be similarly adjusted in the absence of data on phenotypic traits under viability selection. Including as potential parents some individuals that die before reproductive age produces an overall zero-inflated Poisson null model. It is always important to remember that (1) Crow's I represents only the opportunity for selection and not selection itself and (2) the species' biology can lead to random stochasticity in offspring number that is either overdispersed or underdispersed compared with the Poisson (Wright-Fisher) expectation.

Declines in body size of sockeye salmon associated with increased competition in the ocean.

Declining body sizes have been documented for several species of Pacific salmon; however, whether size declines are caused mainly by ocean warming or other ecological factors, and whether they result primarily from trends in age at maturation or changing growth rates remain poorly understood. We quantified changes in mean body size and contributions from shifting size-at-age and age structure of mature sockeye salmon returning to Bristol Bay, Alaska, over the past 60 years. Mean length declined by 3%, corresponding to a 10% decline in mean body mass, since the early 1960s, though much of this decline occurred since the early 2000s. Changes in size-at-age were the dominant cause of body size declines and were more consistent than trends in age structure among the major rivers that flow into Bristol Bay. Annual variation in size-at-age was largely explained by competition among Bristol Bay sockeye salmon and interspecific competition with other salmon in the North Pacific Ocean. Warm winters were associated with better growth of sockeye salmon, whereas warm summers were associated with reduced growth. Our findings point to competition at sea as the main driver of sockeye salmon size declines, and emphasize the trade-off between fish abundance and body size.

Disentangling the causes of age-assortative mating in bird populations with contrasting life-history strategies.

Age shapes fundamental processes related to behaviour, survival and reproduction, where age influences reproductive success, non-random mating with respect to age can magnify or mitigate such effects. Consequently, the correlation in partners' age across a population may influence its productivity. Despite widespread evidence for age-assortative mating, little is known about what drives this assortment and its variation. Specifically, the relative importance of active (same-age mate preference) and passive processes (assortment as a consequence of other spatial or temporal effects) in driving age assortment is not well understood. In this paper, we compare breeding data from a great tit and mute swan population (51- and 31-year datasets, respectively) to tease apart the contributions of pair retention, cohort age structure and active age-related mate selection to age assortment in species with contrasting life histories. Both species show age-assortative mating and variable assortment between years. However, we demonstrate that the drivers of age assortment differ between the species, as expected from their life histories and resultant demographic differences. In great tits, pair fidelity has a weak effect on age-assortative mating through pair retention; variation in age assortment is primarily driven by fluctuations in age structure from variable juvenile recruitment. Age-assortative mating is, therefore, largely passive, with no evidence consistent with active age-related mate selection. In mute swans, age assortment is partly explained by pair retention, but not population age structure, and evidence exists for active age-assortative pairing. This difference is likely to result from shorter life-spans in great tits compared with mute swans, leading to fundamental differences in their population age structure, whereby a larger proportion of great tit populations consist of a single age cohort. In mute swans, age-assortative pairing through mate selection may also be driven by greater age-dependent variation in fitness. The study highlights the importance of considering how different life histories and demographic differences arising from these affect population processes that appear congruent across species. We suggest that future research should focus on uncovering the proximate mechanisms that lead to variation in active age-assortative mate selection (as seen in mute swans); and the consequences of variation in age structure on the ecological and social functioning of wild populations.

PrEP Intervention in the Mitigation of HIV/AIDS Epidemics in China via a Data-Validated Age-Structured Model.

Antiretroviral-based pre-exposure prophylaxis (PrEP) treatment offers a new opportunity for protecting humans against HIV and disrupting current HIV prevention systems. However, implementing this preventive measure has been difficult due to its high cost. In this paper, we propose an age-structured model that incorporates infection ages, HAART (highly active antiretroviral therapy), and PrEP intervention. We investigate the qualitative behavior of the model and find a threshold parameter (the basic reproduction number) that determines the asymptotic stability of equilibria. We validate the model and estimate the parameters by confronting the actual HIV/AIDS data from 2004 to 2018 in China using MCMC (Markov Chain Monte Carlo) method. Furthermore, we investigate the PrEP intervention strategy by using incremental cost-effectiveness and average cost-effectiveness. Our work suggests that PrEP intervention based on the infection characteristics of different age groups can be an effective strategy to eradicate HIV/AIDS epidemics in China.

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.

An age-dependent immuno-epidemiological model with distributed recovery and death rates.

The work is devoted to a new immuno-epidemiological model with distributed recovery and death rates considered as functions of time after the infection onset. Disease transmission rate depends on the intra-subject viral load determined from the immunological submodel. The age-dependent model includes the viral load, recovery and death rates as functions of age considered as a continuous variable. Equations for susceptible, infected, recovered and dead compartments are expressed in terms of the number of newly infected cases. The analysis of the model includes the proof of the existence and uniqueness of solution. Furthermore, it is shown how the model can be reduced to age-dependent SIR or delay model under certain assumptions on recovery and death distributions. Basic reproduction number and final size of epidemic are determined for the reduced models. The model is validated with a COVID-19 case data. Modelling results show that proportion of young age groups can influence the epidemic progression since disease transmission rate for them is higher than for other age groups.

Demographic science aids in understanding the spread and fatality rates of COVID-19.

Governments around the world must rapidly mobilize and make difficult policy decisions to mitigate the coronavirus disease 2019 (COVID-19) pandemic. Because deaths have been concentrated at older ages, we highlight the important role of demography, particularly, how the age structure of a population may help explain differences in fatality rates across countries and how transmission unfolds. We examine the role of age structure in deaths thus far in Italy and South Korea and illustrate how the pandemic could unfold in populations with similar population sizes but different age structures, showing a dramatically higher burden of mortality in countries with older versus younger populations. This powerful interaction of demography and current age-specific mortality for COVID-19 suggests that social distancing and other policies to slow transmission should consider the age composition of local and national contexts as well as intergenerational interactions. We also call for countries to provide case and fatality data disaggregated by age and sex to improve real-time targeted forecasting of hospitalization and critical care needs.

The demographic dividend is more than an education dividend.

The demographic dividend has long been viewed as an important factor for economic development and provided a rationale for policies aiming at a more balanced age structure through birth control and family planning. Assessing the relative importance of age structure and increases in human capital, recent work has argued that the demographic dividend is related to education and has suggested a dominance of improving education over age structure. Here we reconsider the empirical relevance of shifts in the age distribution for development for a panel of 159 countries over the period 1950 to 2015. Based on a flexible model of age-structured human capital endowments, the results document important interactions between age structure and human capital endowments, suggesting that arguments of clear dominance of education over age structure are unwarranted and lead to potentially misleading policy conclusions. An increase in the working-age population share has a strong and significant positive effect on growth, even conditional on human capital, in line with the conventional notion of a demographic dividend. An increase in human capital only has positive growth effects if combined with a suitable age structure. An increasing share of the most productive age groups has an additional positive effect on economic performance. Finally, the results show considerable heterogeneity in the effect of age structure and human capital for different levels of development. Successful policies for sustainable development should take this heterogeneity into account to avoid detrimental implications of a unidimensional focus on human capital without accounting for demography.

Harvesting can stabilise population fluctuations and buffer the impacts of extreme climatic events.

Harvesting can magnify the destabilising effects of environmental perturbations on population dynamics and, thereby, increase extinction risk. However, population-dynamic theory predicts that impacts of harvesting depend on the type and strength of density-dependent regulation. Here, we used logistic population growth models and an empirical reindeer case study to show that low to moderate harvesting can actually buffer populations against environmental perturbations. This occurs because of density-dependent environmental stochasticity, where negative environmental impacts on vital rates are amplified at high population density due to intra-specific resource competition. Simulations from our population models show that even low levels of harvesting may prevent overabundance, thereby dampening population fluctuations and reducing the risk of population collapse and quasi-extinction following environmental perturbations. Thus, depending on the species' life history and the strength of density-dependent environmental drivers, low to moderate harvesting can improve population resistance to increased climate variability and extreme weather expected under global warming.

Age structure affects population productivity in an exploited fish species.

Long-term changes in the age and size structure of animal populations are well documented, yet their impacts on population productivity are poorly understood. Fishery exploitation can be a major driver of changes in population age-size structure because fisheries significantly increase mortality and often selectively remove larger and older fish. Climate change is another potential driver of shifts in the demographic structure of fish populations. Northeast Arctic (NEA) cod is the largest population of Atlantic cod (Gadus morhua) and one of the world's most important commercial fish stocks. This population has experienced considerable changes in population age-size structure over the past century, largely in response to fishing. In this study, we investigate whether changes in spawner age structure have affected population productivity in NEA cod, measured as recruits per spawning stock biomass, over the past 75 years. We find evidence that shifts in age structure toward younger spawners negatively affect population productivity, implying higher recruitment success when the spawning stock is composed of older individuals. The positive effect of an older spawning stock is likely linked to maternal effects and higher reproductive output of larger females. Our results indicate a threefold difference in productivity between the youngest and oldest spawning stock that has been observed since the 1950s. Further, our results suggest a positive effect of environmental temperature and a negative effect of intraspecific cannibalism by older juveniles on population productivity, which partly masked the effect of spawner age structure unless accounted for in the model. Collectively, these findings emphasize the importance of population age structure for the productivity of fish populations and suggest that harvest-induced demographic changes can have negative feedbacks for fisheries that lead to a younger spawning stock. Incorporating demographic data into harvest strategies could thus facilitate sustainable fishery management.

Examination of the interaction between age-specific predation and chronic disease in the Greater Yellowstone Ecosystem.

Predators may create healthier prey populations by selectively removing diseased individuals. Predators typically prefer some ages of prey over others, which may, or may not, align with those prey ages that are most likely to be diseased. The interaction of age-specific infection and predation has not been previously explored and likely has sizable effects on disease dynamics. We hypothesize that predator cleansing effects will be greater when the disease and predation occur in the same prey age groups. We examine the predator cleansing effect using a model where both vulnerability to predators and pathogen prevalence vary with age. We tailor this model to chronic wasting disease (CWD) in mule deer and elk populations in the Greater Yellowstone Ecosystem, with empirical data from Yellowstone grey wolves and cougars. Model results suggest that under moderate, yet realistic, predation pressure from cougars and wolves independently, predators may decrease CWD outbreak size substantially and delay the accumulation of symptomatic deer and elk. The magnitude of this effect is driven by the ability of predators to selectively remove late-stage CWD infections that are likely the most responsible for transmission, but this may not be the age class they typically select. Thus, predators that select for infected young adults over uninfected juveniles have a stronger cleansing effect, and these effects are strengthened when transmission rates increase with increasing prey morbidity. There are also trade-offs from a management perspective-that is, increasing predator kill rates can result in opposing forces on prey abundance and CWD prevalence. Our modelling exploration shows that predators have the potential to reduce prevalence in prey populations when prey age and disease severity are considered, yet the strength of this effect is influenced by predators' selection for demography or body condition. Current CWD management focuses on increasing cervid hunting as the primary management tool, and our results suggest predators may also be a useful tool under certain conditions, but not necessarily without additional impacts on host abundance and demography. Protected areas with predator populations will play a large role in informing the debate over predator impacts on disease.

Assessing Age-Specific Vaccination Strategies and Post-vaccination Reopening Policies for COVID-19 Control Using SEIR Modeling Approach.

As the availability of COVID-19 vaccines, it is badly needed to develop vaccination guidelines to prioritize the vaccination delivery in order to effectively stop COVID-19 epidemic and minimize the loss. We evaluated the effect of age-specific vaccination strategies on the number of infections and deaths using an SEIR model, considering the age structure and social contact patterns for different age groups for each of different countries. In general, the vaccination priority should be given to those younger people who are active in social contacts to minimize the number of infections, while the vaccination priority should be given to the elderly to minimize the number of deaths. But this principle may not always apply when the interaction of age structure and age-specific social contact patterns is complicated. Partially reopening schools, workplaces or households, the vaccination priority may need to be adjusted accordingly. Prematurely reopening social contacts could initiate a new outbreak or even a new pandemic out of control if the vaccination rate and the detection rate are not high enough. Our result suggests that it requires at least nine months of vaccination (with a high vaccination rate > 0.1%) for Italy and India before fully reopening social contacts in order to avoid a new pandemic.

Delays, Masks, the Elderly, and Schools: First Covid-19 Wave in the Czech Republic.

Running across the globe for nearly 2 years, the Covid-19 pandemic keeps demonstrating its strength. Despite a lot of understanding, uncertainty regarding the efficiency of interventions still persists. We developed an age-structured epidemic model parameterized with epidemiological and sociological data for the first Covid-19 wave in the Czech Republic and found that (1) starting the spring 2020 lockdown 4 days earlier might prevent half of the confirmed cases by the end of lockdown period, (2) personal protective measures such as face masks appear more effective than just a realized reduction in social contacts, (3) the strategy of sheltering just the elderly is not at all effective, and (4) leaving schools open is a risky strategy. Despite vaccination programs, evidence-based choice and timing of non-pharmaceutical interventions remains an effective weapon against the Covid-19 pandemic.

Structural identifiability analysis of age-structured PDE epidemic models.

Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well the parameters of a model can be estimated from experimental data. Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.

The age structure of cases as the key of COVID-19 severity: Longitudinal population-based analysis of European countries during 150 days.

AIMS: Over a million confirmed cases of the coronavirus disease (COVID-19) across 16 European countries were observed during the first wave of the pandemic. Epidemiological measures like the case fatality rate (CFR) are generally used to determine the severity of the illness. The aim is to investigate the impact of the age structure of reported cases on the reported CFR and possibilities of its demographic adjustment for a better cross-country comparison (age-standardized CFRs, time delay between cases detection and death). METHODS: This longitudinal study uses prospective, population-based data covering 150 days, starting on the day of confirmation of the 100th case in each country. COVerAGE-DB and the Human Mortality Database were used in this regard. The age-standardized CFRs were calculated with and without the time delay of the number of deaths after the confirmation of the cases. RESULTS: The observed decline in the CFRs at the end of the first wave is partly given by the changes in the age structure of confirmed cases. Using the adjusted (age-standardized) CFRs with time delay, the risk of death among confirmed cases is much more stable in comparison to crude (observed) CFRs. CONCLUSIONS: Preventing the spread of COVID-19 among the elderly is an important way to positively influence the overall fatality rate, decrease the number of deaths, and not overload the health systems. The crude CFRs (still often presented) are not sufficient for a proper evaluation of the development across populations nor as a means of identifying the influencing factors.