Birth Mortality Research Articles

Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size

We are interested in the long-time behavior of a diploid population with sexual reproduction and randomly varying population size, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with competition, weak cooperation and Mendelian reproduction. This stochastic process is indexed by a scaling parameter K that goes to infinity, following a large population assumption. When the individual birth and natural death rates are of order K, the sequence of stochastic processes indexed by K converges toward a new slow-fast dynamics with variable population size. We indeed prove the convergence toward 0 of a fast variable giving the deviation of the population from quasi Hardy-Weinberg equilibrium, while the sequence of slow variables giving the respective numbers of occurrences of each allele converges toward a 2-dimensional diffusion process that reaches (0,0) almost surely in finite time. The population size and the proportion of a given allele converge toward a Wright-Fisher diffusion with stochastically varying population size and diploid selection. We insist on differences between haploid and diploid populations due to population size stochastic variability. Using a non trivial change of variables, we study the absorption of this diffusion and its long time behavior conditioned on non-extinction. In particular we prove that this diffusion starting from any non-trivial state and conditioned on not hitting (0,0) admits a unique quasi-stationary distribution. We give numerical approximations of this quasi-stationary behavior in three biologically relevant cases: neutrality, overdominance, and separate niches.

An Evaluation of Nepal's Demographic Transition (Change in Birth Rates and Death Rates) with Reference to the Frank W. Notestein's Demographic Transition Theory

An Evaluation of Nepal's Demographic Transition (Change in Birth Rates and Death Rates) with Reference to the Frank W. Notestein's Demographic Transition Theory

Age-Structured Population Projection of Bangladesh by Using a Partial Differential Model with Quadratic Polynomial Curve Fitting

In this paper, the age-specific population of Bangladesh based on a linear first order (hyperbolic) partial differential equation which is known as Von-Foerster Equation is studied. Applying quadratic polynomial curve fitting, the total population and population density of Bangladesh are projected for the years 2001 to 2050 based on the explicit upwind finite difference scheme for the age-structured population model based on given data (source: BBS & ICDDR, B) for initial value in the year 2001. For each age-group, the future birth rates and death rates are estimated by using quadratic polynomial curve fitting of the data for the years 2001 to 2012. Quadratic polynomial curve fitting is also used for the boundary value as the (0 - 4) age-group population based on the population size of the age-group for the years 2001 to 2012.

Stochastic grey-box modeling of queueing systems: fitting birth-and-death processes to data

This paper explores grey-box modeling of queueing systems. A stationary birth-and-death (BD) process model is fitted to a segment of the sample path of the number in the system in the usual way. The birth (death) rates in each state are estimated by the observed number of arrivals (departures) in that state divided by the total time spent in that state. Under minor regularity conditions, if the queue length (number in the system) has a proper limiting steady-state distribution, then the fitted BD process has that same steady-state distribution asymptotically as the sample size increases, even if the actual queue-length process is not nearly a BD process. However, the transient behavior may be very different. We investigate what we can learn about the actual queueing system from the fitted BD process. Here we consider the standard $$GI/GI/s$$GI/GI/s queueing model with $$s$$s servers, unlimited waiting room and general independent, non-exponential, interarrival-time and service-time distributions. For heavily loaded $$s$$s-server models, we find that the long-term transient behavior of the original process, as partially characterized by mean first passage times, can be approximated by a deterministic time transformation of the fitted BD process, exploiting the heavy-traffic characterization of the variability.

State-dependent neutral delay equations from population dynamics.

A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.

Global stability analysis of an SIR epidemic model with demographics and time delay on networks

In this paper, a susceptible-infected-recovery (SIR) epidemic model is governed with demographics and time delay on networks. Firstly, the basic reproduction number R0 is derived dependent on birth rate, death rate, recovery rate and transmission rate. The disease-free equilibrium of the model is stable when R0≤1 and unstable when R0>1. Secondly, based on a Jacobian matrix calculated along with the disease-free equilibrium, we find that the system does not occur Hopf branch under the disease-free equilibrium. Thirdly, the global asymptotic stability of a disease-free equilibrium and a unique endemic equilibrium are proved by structuring two Lyapunov functions. Finally, numerical simulations are performed to illustrate the analysis results.

Equations with State-Dependent Delay in Population Biology

A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size.The resulting class of equations includes also neutral delay equations. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE - shift system) is a limiting case of a system of two standard delay equations. We provide results on existence, uniqueness of solutions and linearized stability of equilibria, as well as numerical simulations.

Exponential Stability of Nonmonotone Traveling Waves for Nicholson's Blowflies Equation

This paper is concerned with Nicholson's blowflies equation, a kind of time-delayed reaction-diffusion equation. It is known that when the ratio of birth rate coefficient and death rate coefficient satisfies $1 e$, the equation losses its monotonicity, and its traveling waves are oscillatory when the time-delay $r$ or the wave speed $c$ is large, which causes the study of stability of these nonmonotone traveling waves to be challenging. In this paper, we use the technical weighted energy method to prove that when $e c_*>0$ are exponentially stable, where $c_*>0$ is the minimum wave speed. Here, we allow the traveling wave to be either monotone or nonmonotone with any speed $c>c_*$ and any size of the time-delay $r>0$; however, when $\frac{p}{d}> e^2$ with a smal...

Fitting Birth-Death Processes to Panel Data with Applications to Bacterial DNA Fingerprinting.

Continuous-time linear birth-death-immigration (BDI) processes are frequently used in ecology and epidemiology to model stochastic dynamics of the population of interest. In clinical settings, multiple birth-death processes can describe disease trajectories of individual patients, allowing for estimation of the effects of individual covariates on the birth and death rates of the process. Such estimation is usually accomplished by analyzing patient data collected at unevenly spaced time points, referred to as panel data in the biostatistics literature. Fitting linear BDI processes to panel data is a nontrivial optimization problem because birth and death rates can be functions of many parameters related to the covariates of interest. We propose a novel expectation-maximization (EM) algorithm for fitting linear BDI models with covariates to panel data. We derive a closed-form expression for the joint generating function of some of the BDI process statistics and use this generating function to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one-dimensional integration. This analytical technique yields a computationally efficient and robust optimization algorithm that we implemented in an open-source R package. We apply our method to DNA fingerprinting of Mycobacterium tuberculosis, the causative agent of tuberculosis, to study intrapatient time evolution of IS6110 copy number, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. Our analysis reveals previously undocumented differences in IS6110 birth-death rates among three major lineages of Mycobacterium tuberculosis, which has important implications for epidemiologists that use IS6110 for DNA fingerprinting of Mycobacterium tuberculosis.

A non-autonomous stochastic predator-prey model

The aim of this paper is to consider a non-autonomous predator-prey-like system, with a Gompertz growth law for the prey. By introducing random variations in both prey birth and predator death rates, a stochastic model for the predator-prey-like system in a random environment is proposed and investigated. The corresponding Fokker-Planck equation is solved to obtain the joint probability density for the prey and predator populations and the marginal probability densities. The asymptotic behavior of the predator-prey stochastic model is also analyzed.

Simulação baseada em System Dynamics para avaliação de cenários sobre geração e disposição de resíduos sólidos urbanos

O artigo apresenta o desenvolvimento, validação e experimentação de um modelo de simulação utilizando a metodologia System Dynamics, a qual permite avaliar e analisar cenários acerca da geração e disposição final dos resíduos sólidos urbanos (RSU). Para tanto, levou-se em consideração: a taxa de crescimento vegetativo populacional (nascimentos e mortes), percentual de resíduo sólido urbano enviado para cada tipo de destino final e a quantidade de resíduos gerada por habitante. A validação do modelo foi através da análise de cenários futuros para um determinado município da região sul do Brasil. Para a modelagem e execução do sistema foi utilizado o software Vensim, da Ventana Systems. Com os resultados gerados pelo modelo de simulação, os gestores da área podem, antecipadamente, discutir, avaliar e decidir possíveis medidas necessárias para melhorias ou adaptações na gestão de resíduos sólidos urbanos.

Nuptiality and fertility in Saudi Arabia: An appraisal of census data

Saudi Arabia constitutes bulk of the Arabian Peninsula. Higher birth and lower death rate with higher levels of expectation of life characterizes Saudi Arabian demography. This attempt at appraising nuptiality and fertility is based on censuses. Marriage patterns are changing with higher age at marriage; increasing ever marriage and reducing adolescent marriage, divorces and polygamy. Fertility, was captured from children ever born, parity, and births during 12 months prior to 2004 census and sterility. The children ever born to Saudi Arabian ever married women were 3.8. Women of higher age had higher number of children ever born. Fertility levels remained higher but with a larger proportion of woman at zero parity even among those above 45 years - indication of sterility. Fertility transition was under way as a result of improved female education, value of children, higher age at marriage and reduced infant and child mortality rate. 2013 Production and hosting by Elsevier B.V. on behalf of Middle East Fertility Society.

A TIME-DEPENDENT STUDY OF THE KNOCKOUT QUEUE

We examine the time-dependent behavior of a birth–death process, whose birth rates and death rates are decreasing and increasing, respectively, with respect to the current state. Such models can be used to describe Markovian queueing systems with exponential reneging, where potential arrivals balk with a certain probability that depends on the number of customers observed upon arrival. Our results are derived by interpreting the birth–death process as the queue-length process of what we refer to as the “knockout queue.”

Threshold N-policy for (M, m) degraded machining system with K-heterogeneous servers, standby switching failure and multiple vacations

This paper is concerned with multi-component machining system having online or operating units along with K-type of standby units under the facility of K-heterogeneous servers. The servers switch on one by one when the number of failed units in the system reaches to a predefined threshold policy (Ni for ith server: i = 1, 2, …, K). Once server returns from a vacation, he can leave the system and go for another vacation only if no failed unit available in the system for repair. Whenever any unit fails, it is immediately replaced by an available standby unit. In case when all standbys are used, the system works in degraded mode. The standby units have switching failure probability q. The governing equations are constructed by using appropriate birth-death rates. A cost function has also been constructed to calculate the optimal number of standby units for providing the desired efficiency to the system. The SOR method is employed to find the steady state probabilities, mean number of failed units in the system, reliability and throughput. Numerical results obtained by successive over relaxation (SOR) method are matched by the results evaluated using soft computing approach based on adaptive neuro-fuzzy inference system (ANFIS).

Kinetics of jobs in multi-link cities with migration-driven aggregation process

Immigration has long been a hotly debated issue. The core of this debate is immigrants' impact on local job markets. Some people insist that instead of creating more jobs, immigrants actually take away more jobs thus decrease the living standard of natives. Others argue that the presence of immigrants benefits the society as a whole since they enlarge the labor force and lower the production cost. In this paper, we propose a model describing the migration-driven aggregation behaviors in job markets with foreign immigration, and introduce the method of network and aggregation to look at this issue from a new perspective. We divide the job market in each city into two groups: native and immigrant. And we view each city as a node with l links; each link represents a way of transportation to other cities. Then it is not hard to see that cities with more links tend to be more job concentrated with larger flows of jobs. We assume that both native and immigrant job markets have a migration of jobs within themselves and the native ones have birth rate and death rate of jobs as well. Through analyzing different rates: K1 and K2, initial conditions, and the combined effect of birth rate and death rate, we are able to predict the changes of some variables in the long run. These changes indicate the impact of immigrants on native job markets. Thus provide some helpful information to this issue.

Male Stable Population Tends to be Identical: Evidence from Bangladesh Population Censuses

To investigate the stability situation of population for male of Bangladesh, total males of 1961, 1974, 1981, 1991 and latest 2001 censuses, intercensal growth rates, age specific fertility rates (ASFRs) and stationary population for male at the middle points of various intercensal periods have been used to estimate the intrinsic growth rates, birth rates, death rates and stable population. The estimated intrinsic birth rates and death rates give an idea about the nature of population transition. The male stable population estimated at the mean points of various intercensal periods shows more or less identical age structure. These results lead to the decision of identical male stable population in spite of changing fertility and mortality situations in .

Statistical Laws Governing Fluctuations in Word Use from Word Birth to Word Death

We analyze the dynamic properties of 107 words recorded in English, Spanish and Hebrew over the period 1800–2008 in order to gain insight into the coevolution of language and culture. We report language independent patterns useful as benchmarks for theoretical models of language evolution. A significantly decreasing (increasing) trend in the birth (death) rate of words indicates a recent shift in the selection laws governing word use. For new words, we observe a peak in the growth-rate fluctuations around 40 years after introduction, consistent with the typical entry time into standard dictionaries and the human generational timescale. Pronounced changes in the dynamics of language during periods of war shows that word correlations, occurring across time and between words, are largely influenced by coevolutionary social, technological, and political factors. We quantify cultural memory by analyzing the long-term correlations in the use of individual words using detrended fluctuation analysis.

Fitting birth-and-death queueing models to data

Given measurements of the number of customers in a queueing system over a finite time interval, it is natural to try to fit a stationary birth-and-death process model, because it is remarkably tractable, even when the birth and death rates depend on the state in an arbitrary way. Natural estimators of the birth (death) rate in each state are the observed number of transitions up (down) from that state divided by the total time spent in that state. It is tempting to validate the model by comparing the steady-state distribution of the model based on those estimated rates to the empirical steady-state distribution recording the proportion of time spent in each state. However, it is inappropriate to draw strong conclusions from a close fit to the same data, because these two distributions are necessarily intimately related, even if the model assumptions are not nearly satisfied. We elaborate by (i) establishing stochastic comparisons between these two fitted distributions using likelihood-ratio stochastic ordering and (ii) quantifying their difference.

Institutions and Micro-enterprises Demography: A Study of Selected EU Countries, 1997–2006

Micro-enterprises display diverse patterns with regards to birth rate, death rate, evolution and distribution or density across countries. A large part of the variation of the demography of business enterprises is explained in terms of institutional factors like regulation, corruption, trust, local governance, networks, kinship or family lineage-based business relations. Very high birth and death rates are found in the UK, followed by Portugal, Spain and Italy. High death rates are usually found in the sectors with very high birth rates, as well as in declining sectors, particularly manufacturing, trade and repairing services. A very high churn rate in microenterprises as well as a more balanced size distribution of enterprises in the UK is due to highly competitive market-oriented institutions enabling easier entry, bankruptcy or exit. High density with very low birth and death rates of micro-enterprises are found in Italy due to the particular characteristics of informal institutions of the industrial districts where there is a dense network of relations governing the functioning, entry or exit of enterprises. Survival rate is very high in the UK as compared to the other three countries in the short term but in the long term, over five years, it falls below 50 percent, while Spain and Italy have much higher long-term survival rates.Despite higher short-term survival rates the surviving enterprises of the UK have lower growth of employment as compared to that of the other countries. The greater density of the micro-enterprises in Spain or Portugal makes their business environment more competitive where the inefficient new entrants are quickly weeded out, whereas the remaining ones become more resilient.

Refined age distribution and demographic parameters estimation in nigeria: An indirect approach

Poor census results in terms of age misreporting are becoming too worrisome to planners and policy makers in developing countries, predominantly in Nigeria. This poses serious challenge to the true estimate of basic demographic parameters viz; birth rate, death rate, dependency ratio and expectation of life at birth which are parts of yardstick for measuring growth, development and well being of a nation, hence this study. The study uses data on census which was conducted in 2006. Data analysis was done using Coale and Trussel method of estimating childhood mortality and Coale Demeny model life table. The results showed that male birth and death rates were higher than female birth and death rates. The expectation of life at birth was lower for males than females. Data adjustment using logit transformation through simulation reveals that there is gross age misstatement across all ages, but errors in age reporting are more pronounced among females than males. The patterns of either underreporting or over-reporting of ages are similar for both sexes. Also, there is tendency to under-report ages at ages 15 to 17 years and above 55 years, whereas, gross over-reporting of age are seen in ages between 18 and 55 years. Priority attention should be accorded through public campaign on the need to report true age to all preparatory census activities and population surveys on a regular basis so as to trim down problems of age mis- reporting for healthier demographic parameter estimation.