Threshold Dynamics of a Temperature-Dependent Stage-Structured Mosquito Population Model with Nested Delays

Mosquito-borne diseases remain a significant threat to public health and economics. Since mosquitoes are quite sensitive to temperature, global warming may not only worsen the disease transmission case in current endemic areas but also facilitate mosquito population together with pathogens to establish in new regions. Therefore, understanding mosquito population dynamics under the impact of temperature is considerably important for making disease control policies. In this paper, we develop a stage-structured mosquito population model in the environment of a temperature-controlled experiment. The model turns out to be a system of periodic delay differential equations with periodic delays. We show that the basic reproduction number is a threshold parameter which determines whether the mosquito population goes to extinction or remains persistent. We then estimate the parameter values for Aedes aegypti, the mosquito that transmits dengue virus. We verify the analytic result by numerical simulations with the temperature data of Colombo, Sri Lanka where a dengue outbreak occurred in 2017.     

具反馈控制的时滞阶段结构种群模型的稳定性

研究具反馈控制的时滞阶段结构种群模型,证明了正平衡点的局部渐近稳定性, 并给出了正平衡点全局渐近稳定的充分条件．     

A Periodically-Forced Mathematical Model for the Seasonal Dynamics of Malaria in Mosquitoes

We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate periodic orbits of field-measurable quantities that measure malaria transmission. We integrate this model with an individual-based stochastic simulation model for malaria in humans to compare the effects of insecticide-treated nets (ITNs) and indoor residual spraying (IRS) in reducing malaria transmission, prevalence, and incidence. We show that ITNs are more effective than IRS in reducing transmission and prevalence though IRS would achieve its maximal effects within 2 years while ITNs would need two mass distribution campaigns over several years to do so. Furthermore, the combination of both interventions is more effective than either intervention alone. However, although these interventions reduce transmission and prevalence, they can lead to increased clinical malaria; and all three malaria indicators return to preintervention levels within 3 years after the interventions are withdrawn.     

An Individual-Based Model of Zebrafish Population Dynamics Accounting for Energy Dynamics

Developing population dynamics models for zebrafish is crucial in order to extrapolate from toxicity data measured at the organism level to biological levels relevant to support and enhance ecological risk assessment. To achieve this, a dynamic energy budget for individual zebrafish (DEB model) was coupled to an individual based model of zebrafish population dynamics (IBM model). Next, we fitted the DEB model to new experimental data on zebrafish growth and reproduction thus improving existing models. We further analysed the DEB-model and DEB-IBM using a sensitivity analysis. Finally, the predictions of the DEB-IBM were compared to existing observations on natural zebrafish populations and the predicted population dynamics are realistic. While our zebrafish DEB-IBM model can still be improved by acquiring new experimental data on the most uncertain processes (e.g. survival or feeding), it can already serve to predict the impact of compounds at the population level.     

On a Model for Estimating the Parameter of the Human Reproductive Process

Attempt has been made in this paper to estimate certain parameters (data pertaining to which are either not available or easily reportable) of the human reproductive process as the period of postpartum ammenorrhoea (P.P.A.), number of foetal wastages in between live births etc., using a truncated negative binomial probability model. In view of the hypothesis that the probability of foetal wastages varies from mother to mother, the truncated negative binomial distribution has been compounded by weighing with the best prior Beta distribution of the parameter. Estimation has been made by successive approximation using the method of moments.     

The Effective Population Size of Malaria Mosquitoes: Large Impact of Vector Control

Malaria vectors in sub-Saharan Africa have proven themselves very difficult adversaries in the global struggle against malaria. Decades of anti-vector interventions have yielded mixed results—with successful reductions in transmission in some areas and limited impacts in others. These varying successes can be ascribed to a lack of universally effective vector control tools, as well as the development of insecticide resistance in mosquito populations. Understanding the impact of vector control on mosquito populations is crucial for planning new interventions and evaluating existing ones. However, estimates of population size changes in response to control efforts are often inaccurate because of limitations and biases in collection methods. Attempts to evaluate the impact of vector control on mosquito effective population size (N_e) have produced inconclusive results thus far. Therefore, we obtained data for 13–15 microsatellite markers for more than 1,500 mosquitoes representing multiple time points for seven populations of three important vector species—Anopheles gambiae, An. melas, and An. moucheti—in Equatorial Guinea. These populations were exposed to indoor residual spraying or long-lasting insecticidal nets in recent years. For comparison, we also analyzed data from two populations that have no history of organized vector control. We used Approximate Bayesian Computation to reconstruct their demographic history, allowing us to evaluate the impact of these interventions on the effective population size. In six of the seven study populations, vector control had a dramatic impact on the effective population size, reducing N_e between 55%–87%, the exception being a single An. melas population. In contrast, the two negative control populations did not experience a reduction in effective population size. This study is the first to conclusively link anti-vector intervention programs in Africa to sharply reduced effective population sizes of malaria vectors.     

具脉冲扩散效应的单种群动力学模型

讨论了两斑块间脉冲扩散的单种群动力学模型,利用离散动力系统频闪映射理论,得到了种群持续生存的充分条件．结论31,1~了现实的生物种群动力学性质,也丰富了脉冲微分方程理论．     

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production. We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations.     

Theoretical Population Dynamics Model of a Genetically Transmitted Disease: Sickle-Cell Anaemia

We formulate a realistic demographic model that captures the pattern of inheritance of the S gene, which is responsible for the most common genetic defect, namely, sickle-cell anaemia (SCA), using general pair formations. The model equation is implicitly solved via the Laplace transform technique, while the existence of a unique solution is proved by applying the contraction mapping principle. One of the main results is the boundedness of the solution. A fundamental reason for the persistence of SCA is probably due to the role played by the selective advantage of the abnormal S gene over the normal haemoglobin A in tropical regions, and the fact that carriers are more fertile and survive longer (a property known as hybrid vigor), because they are essentially asymptomatic. We also discuss possible public health policies. 2000 MS Classification: 92D25 · 92D40 · 34C60 · 35F10     

生物协同学,Lorenz模型和种群动力学

由协同学方程出发,可以描述种群的大迁徙,由此又能够得到Lorenz模型,它可以描述两种种群的变化关系．当取绝热近似时,还可以导致种群动力学的不同模型．因此,生物协同学能够深刻揭示不同物种之间,既竞争又协同的复杂的非线性关系．     

Development of a Model For Estimating the Size and Dynamics of the Pet Dog Population

Abstract

A conceptual model was developed to describe the dynamics of the pet dog population. The model synthesizes existing data collected for a variety of purposes to estimate the size of the various components of the pet dog population in Washington and Iowa during 1991. The total population mortality rate was estimated as 12.4% per year. Animal shelters in Washington and Iowa handled 7.6% and euthanized 4.0% of the dog population in those two states. When these estimates were extrapolated to the entire U.S. dog population, the model predicted that the total annual turnover in owned dogs was 14.7%, or 7.71 million dogs, that 4 million dogs were handled by animal shelters, and that 2.1 million were euthanized. It was also estimated that 79% of all female dogs were spayed, that household breeding could be attributed to less than one-fifth (18.7%) of the female dogs in the reproductive pool, and that the number of owners contributing to total dog population turnover through failure to retain their dog (103,453) was approximately three times the number of owners who allowed their female dogs to be bred (32,513).     

Physical Map of the Malaria Vector Anopheles Gambiae

Random cDNA clones, cosmid clones and RAPD polymorphic fragments have been localized by in situ hybridization to the ovarian nurse cell polytene chromosomes of the malaria vector Anopheles gambiae. We thus established 85 molecular markers for 110 sites within the whole A. gambiae polytene chromosome complement. The cDNA clones analyzed were isolated at random, and their exact localizations were determined by in situ hybridization. For 15 of the cDNA clones, a partial nucleotide sequence has been obtained; for nine of them sequence searches in the GenBank database revealed high degrees of similarity with published sequences. The cosmid clones analyzed were obtained as the result of screening with a few of the aforementioned cDNA clones of particular interest, or taken from a small set of randomly isolated cosmid clones. The RAPD clones are polymorphic fragments, potentially diagnostic for the various chromosomal forms of A. gambiae that are currently being analyzed.     

On the Question of Self-Organization of Population Dynamics on Earth

Biophysics - A new mathematical model based on the predator–prey interactions has been proposed. Strictly analytical solution has been found for a system of nonlinear differential equations...     

A Regional Model for Malaria Vector Developmental Habitats Evaluated Using Explicit,Pond-Resolving Surface Hydrology Simulations

Dynamical malaria models can relate precipitation to the availability of vector breeding sites using simple models of surface hydrology. Here, a revised scheme is developed for the VECTRI malaria model, which is evaluated alongside the default scheme using a two year simulation by HYDREMATS, a 10 metre resolution, village-scale model that explicitly simulates individual ponds. Despite the simplicity of the two VECTRI surface hydrology parametrization schemes, they can reproduce the sub-seasonal evolution of fractional water coverage. Calibration of the model parameters is required to simulate the mean pond fraction correctly. The default VECTRI model tended to overestimate water fraction in periods subject to light rainfall events and underestimate it during periods of intense rainfall. This systematic error was improved in the revised scheme by including the a parametrization for surface run-off, such that light rainfall below the initial abstraction threshold does not contribute to ponds. After calibration of the pond model, the VECTRI model was able to simulate vector densities that compared well to the detailed agent based model contained in HYDREMATS without further parameter adjustment. Substituting local rain-gauge data with satellite-retrieved precipitation gave a reasonable approximation, raising the prospects for regional malaria simulations even in data sparse regions. However, further improvements could be made if a method can be derived to calibrate the key hydrology parameters of the pond model in each grid cell location, possibly also incorporating slope and soil texture.     

Influence of Urban Landscapes on Population Dynamics in a Short-Distance Migrant Mosquito: Evidence for the Dengue Vector Aedes aegypti

Background

Dengue viruses are endemic across most tropical and subtropical regions. Because no proven vaccines are available, dengue prevention is primarily accomplished through controlling the mosquito vector Aedes aegypti. While dispersal distance is generally believed to be ∼100 m, patterns of dispersion may vary in urban areas due to landscape features acting as barriers or corridors to dispersal. Anthropogenic features ultimately affect the flow of genes affecting vector competence and insecticide resistance. Therefore, a thorough understanding of what parameters impact dispersal is essential for efficient implementation of any mosquito population suppression program. Population replacement and genetic control strategies currently under consideration are also dependent upon a thorough understanding of mosquito dispersal in urban settings.

Methodology and Principal Findings

We examined the effect of a major highway on dispersal patterns over a 2 year period. A. aegypti larvae were collected on the east and west sides of Uriah Butler Highway (UBH) to examine any effect UBH may have on the observed population structure in the Charlieville neighborhood in Trinidad, West Indies. A panel of nine microsatellites, two SNPs and a 710 bp sequence of mtDNA cytochrome oxidase subunit 1 (CO1) were used for the molecular analyses of the samples. Three CO1 haplotypes were identified, one of which was only found on the east side of the road in 2006 and 2007. AMOVA using mtCO1 and nuclear markers revealed significant differentiation between the east- and west-side collections.

Conclusion and Significance

Our results indicate that anthropogenic barriers to A. aegypti dispersal exist in urban environments and should be considered when implementing control programs during dengue outbreaks and population suppression or replacement programs.     

On the Calibration of a Size-Structured Population Model from Experimental Data

The aim of this work is twofold. First, we survey the techniques developed in Perthame and Zubelli (Inverse Probl 23(3):1037–1052, 2007), Doumic et al. (Inverse Probl 25, 2009) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the experimental data experimental data reported in the classical work of Kubitschek (Biophys J 9(6):792–809, 1969) concerning Escherichia coli in vitro experiments measured by means of a Coulter transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah, FL, USA). Despite the rather old measurement technology, the reconstructed division rates still display potentially useful biological features.