Fisheries have reduced the abundances of large piscivores-such as gadids (cod, pollock, etc.) and tunas-in ecosystems around the world. Fisheries also target smaller species-such as herring, capelin, ...and sprat-that are important parts of the piscivores' diets. It has been suggested that harvesting of these so-called forage fish will harm piscivores. Multispecies models used for fisheries assessments typically ignore important facets of fish community dynamics, such as individual-level bioenergetics and/or size structure. We test the effects of fishing for both forage fish and piscivores using a dynamic, multitrophic, size-structured, bioenergetics model of the Baltic Sea. In addition, we analyze historical patterns in piscivore-biomass declines and fishing mortalities of piscivores and forage fish using global fish-stock assessment data. Our community-dynamics model shows that piscivores benefit from harvesting of their forage fish when piscivore fishing mortality is high. With substantial harvesting of forage fish, the piscivores can withstand higher fishing mortality. On the other hand, when piscivore fishing mortality is low, piscivore biomass decreases with more fishing of the forage fish. In accordance with these predictions, our statistical analysis of global fisheries data shows a positive interaction between the fishing mortalities of forage-fish stocks and piscivore stocks on the strength of piscivore-biomass declines. While overfishing of forage fish must be prevented, our study shows that reducing fishing pressures on forage fish may have unwanted negative side effects on piscivores. In some cases, decreasing forage-fish exploitation could cause declines, or even collapses, of piscivore stocks.
This paper is concerned with the mathematical analysis of an age-structured multi-group heroin epidemic model, which can be used to describe the spread of heroin habituation and addiction in ...heterogeneous environment. Under general assumptions on the different level of susceptibility and the relapse to frequent heroin use, we establish sharp criteria for heroin spreading and vanishing. We rigorously investigate the well-posedness of the model, the existence of equilibria, the asymptotic smoothness of solution orbits, and the global stability of equilibria. Specifically, we rigorously show that the drug-free equilibrium is globally asymptotically stable if a threshold value ℜ0 is less than one, and the unique drug-endemic equilibrium is globally attractive if ℜ0 is greater than one. In the proofs of global stability of equilibria, we construct suitable Lyapunov functions by using a graph-theoretic method.
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.
•Age-structured model plays a crucial role in identifying effective interventions.•Population and social structure influence the transmission of COVID-19.•Reporting of probable cases aids in controlling the spread of the disease.•Optimal control theory guides in vaccine allocation strategy given limited resources.
The fall armyworm (Spodoptera frugiperda Smith & Abbot, 1797, Lepidoptera, Noctuidae) is a widespread agricultural pest native of the Americas. It is a lepidopteran pest with the ability to consume ...an enormous variety of crops. There are several control strategies, including natural enemies employed to control the pest, particularly egg parasitoids and genetically modified crops with Bacillus thuringiensis Berliner, 1915, Bacillaceae (Bt) toxins. However, the constant use of Bt crops has allowed the emergence of positive selection pressure to create pests increasingly resistant to the toxins. Furthermore, female moths can lay eggs in layers and deposit scales to enhance their defences against egg parasitoids. In the present work, we intend to understand how (i) the attack rate of the parasitoid, (ii) the degree of vulnerability of the eggs to parasitism, and (iii) the mortality caused by Bt toxins affect crop production and the overall dynamics. We developed a tritrophic crop-pest-parasitoid mathematical model to study the fall armyworm dynamics focusing on crop density. Our findings indicate that crop production decreases by approximately 60.03% in the absence of parasitoids. We discuss the results regarding pest resistance to Bt toxins, pest defence against parasitism, and the selection of parasitoids for pest control, and propose potential extensions for future work.
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•We developed a tritrophic crop-pest-parasitoid model structured in stages.•The model considers crops with Bt toxins and pest defences against parasitism.•The presence of parasitoids reduced the loss of production by about 60.03%.•High parasitoid attack or high Bt mortality reduces the pest population.•Counter-intuitively the decrease in pest defences increased the pest population.
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important ...instance of the simultaneously structured model - an actively studied topic in statistics and machine learning. In the noiseless case, matching upper and lower bounds on sample complexity are established for the exact recovery of sparse vectors and for stable estimation of approximately sparse vectors, respectively. In the noisy case, upper and matching minimax lower bounds for estimation error are obtained. We also consider the debiased sparse group Lasso and investigate its asymptotic property for the purpose of statistical inference. Finally, numerical studies are provided to support the theoretical results.
•We incorporate the vaccination in a two age-class model of polio dynamics.•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 and the mandatory vaccination policy is therefore needed to achieve a complete eradication.•The results are not sensitive to parameter perturbations.
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.
In this paper, we investigate the local exact controllability of an age structured problem modelling the ability of malaria vectors to shift their biting time to avoid the stressful environmental ...conditions generated by the use of indoor residual spraying (IRS) and insecticide-treated nets (ITNs). We establish a new Carleman’s inequality for our age diffusive model with nonlocal birth process and periodic biting time boundary conditions. Some estimates of the theory of parabolic boundary value problems in Lk are used to get the controllability.
Growth – the way that fish get bigger as they get older – is one component of the population models used in fisheries stock assessments. I review current practice related to this component in ...age-structured models, discussing how growth is specified, its functions in the stock assessment model, and how growth-related data are used. I then discuss some associated problems and suggest that (a) we should be cautious about assuming that all fishery selectivities are size-based, and that an age–size sample is always random at size; (b) the jury is still out on the question of whether growth variation by phenotype is a useful model feature; (c) when growth is time-varying, conditional age-at-size data might better used outside the model (as an age–size key); and (d) that it is often difficult to extract much growth information from size composition data. I conclude by presenting a strategy for addressing the structural, procedural, and statistical decisions that must be made in finding the growth model best suited to our data.
This paper is devoted to the existence of traveling waves in an age-structured nonlocal dispersal model derived from an epidemic model with vertical infection. The Schauder’s fixed point theorem is ...employed to show that the traveling wave solution exists for all c>c∗.
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