ABSTRACT This paper establishes a rigorous foundation for population policy by applying intertemporal optimization theory to derive the optimal trade-off between population growth (or decline) and age-structure fluctuations caused by fertility rate changes. The model is based on the McKendrick-von Foerster partial differential equation, with an objective functional representing the discounted adaptation costs associated with the net reproduction rate. To enhance analytical tractability, we assume concentrated vitality rates. Our findings suggest that, over short-time horizons, an initial under- or overshooting of the net reproduction rate is optimal, while over longer horizons, an oscillating net reproduction rate emerges as the best trajectory. Numerical simulations using a stylized population structure illustrate how variations in the net reproduction rate influence the total population dynamics and age-group distributions over time. This study highlights the critical role of optimization in designing adaptive and sustainable population policies.

ABSTRACT We introduce a nonparametric bootstrap procedure based on a dynamic factor model to construct pointwise prediction intervals for period life-table death counts. The age distribution of death counts is an example of constrained data, which are nonnegative and have a constrained integral. A centered log-ratio transformation is used to remove the constraints. With a time series of unconstrained data, we introduce our bootstrap method to construct prediction intervals, thereby quantifying forecast uncertainty. The bootstrap method utilizes a dynamic factor model to capture both nonstationary and stationary patterns through a two-stage functional principal component analysis. To capture parameter uncertainty, the estimated principal component scores and model residuals are sampled with replacement. Using the age- and sex-specific life-table deaths for Australia and the United Kingdom, we study the empirical coverage probabilities and compare them with the nominal ones. The bootstrap method has superior interval forecast accuracy, especially for the one-step-ahead forecast horizon.

ABSTRACT Existence and uniqueness of a global positive solution are proved for a stochastic Nicholson’s equation of a blowfly population with delay and Lévy noise. The first-order moment of the solution is bounded and the mean of its second moment is finite. A threshold quantity depending on the parameters is involved in the drift, the diffusion parameter, and the magnitude and distribution of jumps. The blowfly population goes extinct exponentially fast when . It persists when The case does not allow for knowing whether the population goes extinct or not.

ABSTRACT Taylor’s law states that the spatial variance of the population density varies as the power function of the mean population density. This law is tested on daily Covid-19 infection density for five periods between February 25, 2020 and March 15, 2021. The Italian provinces are grouped by geography into three ensembles. A simultaneous-equation model accounts for correlations between the ensembles, between Italian provinces within each ensemble, and for temporal autocorrelations. The selected periods show ensembles with all Taylor’s law slopes below 2 (reflecting State interventions at the national level), or all above 2 (reflecting interventions at the local level), or some ensembles above while others were below. Slope of Taylor’s law and average density trend indicate whether the infection density is highly concentrated in a few provinces (when the slope is greater than 2 with increasing density, and when the slope is less than 2 with decreasing density) or spread evenly among all provinces in an ensemble (when the slope is greater than 2 with decreasing density, and when the slope is less than 2 with increasing density), which allows the government and epidemiologists to design disease control policies for targeted provinces and ensembles in Italy.

ABSTRACT The Moore-Bilikam distribution is convenient for survival analysis. The estimation of its parameters and its reliability function is performed by maximum likelihood, expectation-maximization, stochastic expectation-maximization, and the Bayesian method. The data are progressively censored of type II (samples are removed randomly from the experiment). Simulation shows that the expectation-maximization estimator of the parameter and the Bayesian-shrinkage estimator of the reliability function are the most efficient (with the minimum mean square error) when they are based on the Weibull and the Pareto distributions, which are specific cases of the Moore-Bilikam distribution. Bayesian and maximum likelihood estimations using the Moore-Bilikam distribution under type-II progressive censoring allow for fitting empirical failure times of an insulating fluid between two electrodes and the resistance of single carbon fibers. The associated reliability functions are estimated by each method.

ABSTRACT To estimate the population mean when sampling a heterogeneous population and in the absence of a priori information on auxiliary variables, exponential-ratio multivariate estimators are associated under double stratified sampling with two auxiliary variables. Their biases and mean square errors are expressed and simulated. These mean square errors are smaller (the efficiencies are higher) than those of the sample mean estimator and those of other ratio estimators when the correlation between the study and the auxiliary variables exceeds 0.1 in absolute value. In particular, the proposed estimators are more efficient for low correlations between the study and the auxiliary variables. The gain in efficiency reaches a factor of 230.4% on an empirical dataset where the study variable is weakly correlated with each of the two auxiliary variables, and 182.1% on another empirical dataset where it is strongly correlated.

ABSTRACT Blowflies use open wounds or the accumulation of feces or urine in wool to lay their eggs. The larvae that emerge cause lesions in the host sheep, which can lead to death. They are found in Australia, New Zealand, and the United Kingdom. Nicholson’s model describes the population dynamics of the Australian blowfly (Lucilia Cuprina). It incorporates environmental variation. The extinction of these flies depends on the time to oviposition and the time between generations. The Lyapunov function, which is positive with a negative derivative, provides the condition for the stability of the equilibrium point: the oviposition period must be sufficiently short, because the shorter it is, the more it favors the extinction of the species. The zero solution is the only equilibrium point, synonymous with the extinction of the population. Another species of blowfly, Lucilia Sericata, also attacks sheep in Australia. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to share same mitochondrial DNA sequences, although the two species are distinct. Presumably to avoid competition between them. the egg-laying time of each species does not occur at the same time of year: L. Sericata prefers warmer months, thus in summer, while L. Cuprina is mainly active in autumn. Laying of eggs in different months allows avoiding competition between these species. This also binds them together. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations, provided they do not adapt.

ABSTRACT Among children under five in Nigeria, in the year 2018, the prevalence of diarrhea was 13%, that of acute respiratory infections 3%, and that of stunting 37%. A shared-component model highlights geographic variations in the comorbidities of these diseases. The data are from the 2018 Nigeria Demographic and Health Survey. The majority of states in northern Nigeria presented clusters of higher risk for comorbidities of any pair of the three diseases. Compared with mothers with primary education or less, mothers with secondary education were 1.4 times less likely to have two or three of these diseases at the same time, and women with tertiary education 2.0 times less. Compared to childless women of the same age, mothers were 1.6 times less when aged 20–29, 1.9 times less when aged 30–39, and 2.0 times less when aged 40–49. Access to a protected water source reduced the risk by a factor of 1.3. Girls under age five were 1.2 times less likely than boys of that age to have two or three of these diseases at the same time. This factor was the same for breastfed children compared to those who were not breastfed.

ABSTRACT In a catalytic branching random walk on a multidimensional lattice, with arbitrary finite total number of catalysts, in supercritical regime, when the vector coordinates of the random walk jump are assumed independent (or close to independent) to one another and have semi-exponential distributions, a limit theorem provides the almost sure normalized locations of the particles at the boundary between populated and empty areas. Contrary to the case of random walk increments with light distribution tails, the normalizing factor grows faster than linearly over time. The limit shape of the front in the case of semi-exponential tails is no longer convex, as it is in the case of light tails.

ABSTRACT Trichomoniasis is a sexually transmitted disease caused by an infection from the parasite Trichomonas vaginalis. A model of its transmission shows a backward bifurcation when the basic reproduction number is less than one. A stable disease-free equilibrium co-exists with a stable endemic equilibrium with the consequence that the disease may invade the population even when . The backward bifurcation is due to reinfection among the people who have recovered. In the absence of a backward bifurcation and when , the disease-free equilibrium has global asymptotic stability. In the absence of reinfection, the model has a unique global asymptotically stable endemic equilibrium when . Contact rates are the major parameters in the persistence of the disease, compared to rates of recovery after treatment, infectiousness of asymptomatic individuals, and rates of reinfection.