Malaria model with periodic mosquito birth and death rates

In this paper, we introduce a model of malaria, a disease that involves a complex life cycle of parasites, requiring both human and mosquito hosts. The novelty of the model is the introduction of periodic coefficients into the system of one-dimensional equations, which account for the seasonal variations (wet and dry seasons) in the mosquito birth and death rates. We define a basic reproduction number R(0) that depends on the periodic coefficients and prove that if R(0)<1 then the disease becomes extinct, whereas if R(0)>1 then the disease is endemic and may even be periodic.     

Persistence in periodic and almost periodic Lotka-Volterra systems

It is shown that a strongly self-regulating (or resource limited) Lotka-Volterra population system can persist in a periodic or almost periodic environment if and only if the system tracks the environmental variations.     

The meaning of birth and death (in macroevolutionary birth-death models)

Birth–death models are central to much macroevolutionary theory. The fundamental parameters of these models concern durations. Different species concepts realize different species durations because they represent different ideas of what birth (speciation) and death (extinction) mean. Here, we use Cenozoic macroperforate planktonic foraminifera as a case study to ask: what are the dynamical consequences of changing the definition of birth and death? We show strong evidence for biotic constraints on diversification using evolutionary species, but less with morphospecies. Discussing reasons for this discrepancy, we emphasize that clarity of species concept leads to clarity of meaning when interpreting macroevolutionary birth–death models.     

A stochastic discrete generation birth,continuous death population growth model and its approximate solution

This paper describes a single species growth model with a stochastic population size dependent number of births occurring at discrete generation times and a continuous population size dependent death rate. An integral equation for a suitable transformation of the limiting population size density function is not in general soluble, but a Gram-Charlier representation procedure, previously used in storage theory, is successfully extended to cover this problem. Examples of logistic and Gompertz type growth are used to illustrate the procedure, and to compare with growth models in random environments. Comments on the biological consequences of these models are also given.Currently at Department of Mathematics, University of MarylandWork partially supported by the Danish Natural Science Research Council and Monash University     

Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays

This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.     

High-throughput quantification of microbial birth and death dynamics using fluorescence microscopy

Background: Microbes live in dynamic environments where nutrient concentrations fluctuate. Quantifying fitness in terms of birth rate and death rate in a wide range of environments is critical for understanding microbial evolution and ecology. Methods: Here, using high-throughput time-lapse microscopy, we have quantified how Saccharomyces cerevisiae mutants incapable of synthesizing an essential metabolite (auxotrophs) grow or die in various concentrations of the required metabolite. We establish that cells normally expressing fluorescent proteins lose fluorescence upon death and that the total fluorescence in an imaging frame is proportional to the number of live cells even when cells form multiple layers. We validate our microscopy approach of measuring birth and death rates using flow cytometry, cell counting, and chemostat culturing. Results: For lysine-requiring cells, very low concentrations of lysine are not detectably consumed and do not support cell birth, but delay the onset of death phase and reduce the death rate compared to no lysine. In contrast, in low hypoxanthine, hypoxanthine-requiring cells can produce new cells, yet also die faster than in the absence of hypoxanthine. For both strains, birth rates under various metabolite concentrations are better described by the sigmoidal-shaped Moser model than the well-known Monod model, while death rates can vary with metabolite concentration and time. Conclusions: Our work reveals how time-lapse microscopy can be used to discover non-intuitive microbial birth and death dynamics and to quantify growth rates in many environments.     

Factors associated with birth rate and live birth rate in multi-male breeding groups of rhesus monkeys

Reproductive records of 284 female rhesus monkeys housed in six multimale corrals at the California Primate Research Center were examined for the birth seasons 1977–1982 to determine possible associations between the probability of birth or live birth and female age, parity, origin, parturition in the previous season, infant birth date, and infant birth date in previous season. Multiple logistic regression analysis was used to identify and quantitate the effects of factors on the probability of birth or live birth, while controlling for the possibly confounding effects of other factors in the model. Females who had infants early in the previous season were 2.5 times as likely to give birth as those who had infants late in the previous season. Females with two or three previous births were 2.1 times as likely to give birth, and those with four or five previous births were 6.7 times as likely to give birth as were females with no or one previous birth. Controlling for other factors (age, parity, and timing of birth in the previous season), corralborn females were 3.3 times as likely to give birth as either wild-caught or domestic-born monkeys not native to the corrals. Domestic-born females who were not corral natives were 0.3 times as likely to have live births as wild-caught females. Births late in the season were 1.8 times as likely to result in live infants as births early in the season.     

Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients

In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations.     

Predator-prey systems with a perturbed periodic carrying capacity

In this paper we perturb the constant carrying capacity of a predatorprey model. Non-critical cases and critical cases are investigated for existence and stability of periodic solutions.     

Modelling of drug receptor interaction with birth and death processes

Stochastic modelling of drug receptor interaction at the neuromuscular junction with birth and death processes is presented. Systems with only one drug and two drugs interacting are investigated separately. The total number of receptors is assumed finite and only single receptor binding is considered. It has been possible to obtain exact analytical solutions to forward Kolmogorov equations yielding the transition probability densities and the associated probability generating functions.     

Persistence and permanence in a metapopulation model with space-limited recruitment

In this paper we analyze a metapopulation model with space-limited recruitment. The model describes the population dynamics of sessile adult and planktonic larvae in a common larval pool. We introduce the basic reproduction number of each species which is the expected number of future larvae reproduced by one larva. We consider the conditions for the persistence of the multi-species and multi-habitats model and the permanence of the single-species model. Subsequently, we consider the conditions for the existence of the non-trivial steady state of the single-species model and its global stability, and the permanence of the two species and two habitats model.     

Dynamical behavior of a hepatitis B virus transmission model with vaccination

Hepatitis B virus (HBV) infection is a globally health problem. In 2005, the WHO Western Pacific Regional Office set a goal of reducing chronic HBV infection rate to less than 2% among children five years of age by 2012, as an interim milestone towards the final goal of less than 1%. Many countries made some plans (such as free HBV vaccination program for all neonates in China now) to control the transmission HBV. We develop a model to explore the impact of vaccination and other controlling measures of HBV infection. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R₀≤1, and a globally asymptotically stable endemic equilibrium when R₀>1. Numerical simulation results show that the vaccination is a very effective measure to control the infection and they also give some useful comments on controlling the transmission of HBV.     

Exploring the power of Bayesian birth‐death skyline models to detect mass extinction events from phylogenies with only extant taxa

Mass extinction events (MEEs), defined as significant losses of species diversity in significantly short time periods, have attracted the attention of biologists because of their link to major environmental change. MEEs have traditionally been studied through the fossil record, but the development of birth‐death models has made it possible to detect their signature based on extant‐taxa phylogenies. Most birth‐death models consider MEEs as instantaneous events where a high proportion of species are simultaneously removed from the tree (“single pulse” approach), in contrast to the paleontological record, where MEEs have a time duration. Here, we explore the power of a Bayesian Birth‐Death Skyline (BDSKY) model to detect the signature of MEEs through changes in extinction rates under a “time‐slice” approach. In this approach, MEEs are time intervals where the extinction rate is greater than the speciation rate. Results showed BDSKY can detect and locate MEEs but that precision and accuracy depend on the phylogeny's size and MEE intensity. Comparisons of BDSKY with the single‐pulse Bayesian model, CoMET, showed a similar frequency of Type II error and neither model exhibited Type I error. However, while CoMET performed better in detecting and locating MEEs for smaller phylogenies, BDSKY showed higher accuracy in estimating extinction and speciation rates.     

An SIS patch model with variable transmission coefficients

In this paper, an SIS patch model with non-constant transmission coefficients is formulated to investigate the effect of media coverage and human movement on the spread of infectious diseases among patches. The basic reproduction number R₀ is determined. It is shown that the disease-free equilibrium is globally asymptotically stable if R₀?1, and the disease is uniformly persistent and there exists at least one endemic equilibrium if R₀>1. In particular, when the disease is non-fatal and the travel rates of susceptible and infectious individuals in each patch are the same, the endemic equilibrium is unique and is globally asymptotically stable as R₀>1. Numerical calculations are performed to illustrate some results for the case with two patches.