A Stochastic Population Dynamics Model for Aedes Aegypti: Formulation and Application to a City with Temperate Climate

Aedes aegypti is the main vector for dengue and urban yellow fever. It is extended around the world not only in the tropical regions but also beyond them, reaching temperate climates. Because of its importance as a vector of deadly diseases, the significance of its distribution in urban areas and the possibility of breeding in laboratory facilities, Aedes aegypti is one of the best-known mosquitoes. In this work the biology of Aedes aegypti is incorporated into the framework of a stochastic population dynamics model able to handle seasonal and total extinction as well as endemic situations. The model incorporates explicitly the dependence with temperature. The ecological parameters of the model are tuned to the present populations of Aedes aegypti in Buenos Aires city, which is at the border of the present day geographical distribution in South America. Temperature thresholds for the mosquito survival are computed as a function of average yearly temperature and seasonal variation as well as breeding site availability. The stochastic analysis suggests that the southern limit of Aedes aegypti distribution in South America is close to the 15^∘C average yearly isotherm, which accounts for the historical and current distribution better than the traditional criterion of the winter (July) 10°C isotherm.     

一个具有随机传染率艾滋病模型的渐近行为(英文)

研究了艾滋病传播的随机模型.我们给出了一个条件,在这个条件下,无论环境干扰有多强,随机Logistic方程的平凡解是渐近稳定的.我们的结论与Roberts和Saha的结论构成对艾滋病传播模型的一个完整的分析.     

Transmission selects for HIV-1 strains of intermediate virulence: a modelling approach

Recent data shows that HIV-1 is characterised by variation in viral virulence factors that is heritable between infections, which suggests that viral virulence can be naturally selected at the population level. A trade-off between transmissibility and duration of infection appears to favour viruses of intermediate virulence. We developed a mathematical model to simulate the dynamics of putative viral genotypes that differ in their virulence. As a proxy for virulence, we use set-point viral load (SPVL), which is the steady density of viral particles in blood during asymptomatic infection. Mutation, the dependency of survival and transmissibility on SPVL, and host effects were incorporated into the model. The model was fitted to data to estimate unknown parameters, and was found to fit existing data well. The maximum likelihood estimates of the parameters produced a model in which SPVL converged from any initial conditions to observed values within 100-150 years of first emergence of HIV-1. We estimated the 1) host effect and 2) the extent to which the viral virulence genotype mutates from one infection to the next, and found a trade-off between these two parameters in explaining the variation in SPVL. The model confirms that evolution of virulence towards intermediate levels is sufficiently rapid for it to have happened in the early stages of the HIV epidemic, and confirms that existing viral loads are nearly optimal given the assumed constraints on evolution. The model provides a useful framework under which to examine the future evolution of HIV-1 virulence.     

Restriction of HIV-1 Genotypes in Breast Milk Does Not Account for the Population Transmission Genetic Bottleneck That Occurs following Transmission

Background

Breast milk transmission of HIV-1 remains a major route of pediatric infection. Defining the characteristics of viral variants to which breastfeeding infants are exposed is important for understanding the genetic bottleneck that occurs in the majority of mother-to-child transmissions. The blood-milk epithelial barrier markedly restricts the quantity of HIV-1 in breast milk, even in the absence of antiretroviral drugs. The basis of this restriction and the genetic relationship between breast milk and blood variants are not well established.

Methodology/Principal Findings

We compared 356 HIV-1 subtype C gp160 envelope (env) gene sequences from the plasma and breast milk of 13 breastfeeding women. A trend towards lower viral population diversity and divergence in breast milk was observed, potentially indicative of clonal expansion within the breast. No differences in potential N-linked glycosylation site numbers or in gp160 variable loop amino acid lengths were identified. Genetic compartmentalization was evident in only one out of six subjects in whom contemporaneously obtained samples were studied. However, in samples that were collected 10 or more days apart, six of seven subjects were classified as having compartmentalized viral populations, highlighting the necessity of contemporaneous sampling for genetic compartmentalization studies. We found evidence of CXCR4 co-receptor using viruses in breast milk and blood in nine out of the thirteen subjects, but no evidence of preferential localization of these variants in either tissue.

Conclusions/Significance

Despite marked restriction of HIV-1 quantities in milk, our data indicate intermixing of virus between blood and breast milk. Thus, we found no evidence that a restriction in viral genotype diversity in breast milk accounts for the genetic bottleneck observed following transmission. In addition, our results highlight the rapidity of HIV-1 env evolution and the importance of sample timing in analyses of gene flow.     

The Genealogical Population Dynamics of HIV-1 in a Large Transmission Chain: Bridging within and among Host Evolutionary Rates

Transmission lies at the interface of human immunodeficiency virus type 1 (HIV-1) evolution within and among hosts and separates distinct selective pressures that impose differences in both the mode of diversification and the tempo of evolution. In the absence of comprehensive direct comparative analyses of the evolutionary processes at different biological scales, our understanding of how fast within-host HIV-1 evolutionary rates translate to lower rates at the between host level remains incomplete. Here, we address this by analyzing pol and env data from a large HIV-1 subtype C transmission chain for which both the timing and the direction is known for most transmission events. To this purpose, we develop a new transmission model in a Bayesian genealogical inference framework and demonstrate how to constrain the viral evolutionary history to be compatible with the transmission history while simultaneously inferring the within-host evolutionary and population dynamics. We show that accommodating a transmission bottleneck affords the best fit our data, but the sparse within-host HIV-1 sampling prevents accurate quantification of the concomitant loss in genetic diversity. We draw inference under the transmission model to estimate HIV-1 evolutionary rates among epidemiologically-related patients and demonstrate that they lie in between fast intra-host rates and lower rates among epidemiologically unrelated individuals infected with HIV subtype C. Using a new molecular clock approach, we quantify and find support for a lower evolutionary rate along branches that accommodate a transmission event or branches that represent the entire backbone of transmitted lineages in our transmission history. Finally, we recover the rate differences at the different biological scales for both synonymous and non-synonymous substitution rates, which is only compatible with the ‘store and retrieve’ hypothesis positing that viruses stored early in latently infected cells preferentially transmit or establish new infections upon reactivation.     

A structure-based approach to a synthetic vaccine for HIV-1

The generation of neutralizing antibodies by peptide immunization is dependent on achieving conformational compatibility between antibodies and native protein. Consequently, approaches are needed for developing conformational mimics of protein neutralization sites. We replace putative main-chain hydrogen bonds (NH --> O=CRNH) with a hydrazone link (N-N=CH-CH(2)CH(2)) and scan constrained peptides for fit with neutralizing monoclonal antibodies (MAbs). To explore this approach, a V3 MAb 58.2 that potently neutralizes T-cell lab-adapted HIV-1(MN) was used to identify a cyclic peptide, [JHIGPGR(Aib)F(D-Ala)GZ]G-NH(2) (loop 5), that binds with >1000-fold higher affinity than the unconstrained peptide. NMR structural studies suggested that loop 5 stabilized beta-turns at GPGR and R(Aib)F(D-Ala) in aqueous solvent implying considerable conformational mimicry of a Fab 58.2 bound V3 peptide determined by X-ray crystallography [Stanfield, R. L. et al. (1999) Structure 142, 131-142]. Rabbit polyclonal antibodies (PAbs) generated to loop 5 but not to the corresponding uncyclized peptide bound the HIV-1(MN) envelope glycoprotein, gp120. When individual rabbit antisera were scanned with linear and cyclic peptides, further animal-to-animal differences in antibody populations were characterized. Loop 5 PAbs that most closely mimicked MAb 58.2 neutralized HIV-1(MN) with similar potency. These results demonstrate the remarkable effect that conformation can have on peptide affinity and immunogenicity and identify an approach that can be used to achieve these results. The implications for synthetic vaccine and HIV-1 vaccine research are discussed.     

A Stochastic Model for Surname Evolution

Surnames are inherited in much the same way as biological traits like alleles of one locus. Assuming the heritability of surnames, a simple stochastic model for X, the total number of occurrences of a surname, the Consul distribution defined by the probability mass function: for x = 1, 2, 3,… and zero otherwise and where either (i) m is a positive integer when 0 ≤ θ ≤ 1 such that θ ≦ mθ ≦ 1, or (ii) m≤0, θ ≤0 such that mθ 1, can be arrived at by considering the branching process mechanism. Some applications of the model to real data are also considered.     

Inefficient Vaginal Transmission of Tenofovir-Resistant HIV-1

Transmission of drug-resistant HIV has been postulated to be a threat to current first-line antiretroviral therapy (ART) regimens and the efficacy of several antiretroviral-based preexposure prophylaxis (PrEP) strategies being tested. Here we evaluated the effect of the common tenofovir (TFV) resistance mutation K65R on vaginal HIV transmission. Our results demonstrate that despite no overt loss of overall replication competence in vivo, this mutation results in significantly reduced mucosal transmission. When transmitted, the mutant virus eventually reverted to the wild type in 2 of 3 animals examined.     

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, , however, is not known. Application of the quasispecies theory to determine poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and . We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated to be substitutions/site/replication, ∼2–6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.     

A Multi-Area Stochastic Model for a Covert Visual Search Task

Decisions typically comprise several elements. For example, attention must be directed towards specific objects, their identities recognized, and a choice made among alternatives. Pairs of competing accumulators and drift-diffusion processes provide good models of evidence integration in two-alternative perceptual choices, but more complex tasks requiring the coordination of attention and decision making involve multistage processing and multiple brain areas. Here we consider a task in which a target is located among distractors and its identity reported by lever release. The data comprise reaction times, accuracies, and single unit recordings from two monkeys’ lateral interparietal area (LIP) neurons. LIP firing rates distinguish between targets and distractors, exhibit stimulus set size effects, and show response-hemifield congruence effects. These data motivate our model, which uses coupled sets of leaky competing accumulators to represent processes hypothesized to occur in feature-selective areas and limb motor and pre-motor areas, together with the visual selection process occurring in LIP. Model simulations capture the electrophysiological and behavioral data, and fitted parameters suggest that different connection weights between LIP and the other cortical areas may account for the observed behavioral differences between the animals.     

Dual Processing Model for Medical Decision-Making: An Extension to Diagnostic Testing

Dual Processing Theories (DPT) assume that human cognition is governed by two distinct types of processes typically referred to as type 1 (intuitive) and type 2 (deliberative). Based on DPT we have derived a Dual Processing Model (DPM) to describe and explain therapeutic medical decision-making. The DPM model indicates that doctors decide to treat when treatment benefits outweigh its harms, which occurs when the probability of the disease is greater than the so called “threshold probability” at which treatment benefits are equal to treatment harms. Here we extend our work to include a wider class of decision problems that involve diagnostic testing. We illustrate applicability of the proposed model in a typical clinical scenario considering the management of a patient with prostate cancer. To that end, we calculate and compare two types of decision-thresholds: one that adheres to expected utility theory (EUT) and the second according to DPM. Our results showed that the decisions to administer a diagnostic test could be better explained using the DPM threshold. This is because such decisions depend on objective evidence of test/treatment benefits and harms as well as type 1 cognition of benefits and harms, which are not considered under EUT. Given that type 1 processes are unique to each decision-maker, this means that the DPM threshold will vary among different individuals. We also showed that when type 1 processes exclusively dominate decisions, ordering a diagnostic test does not affect a decision; the decision is based on the assessment of benefits and harms of treatment. These findings could explain variations in the treatment and diagnostic patterns documented in today’s clinical practice.     

A Stochastic Model for Coupled Enzyme System

The molecular biology of transformed cancer cells singles out key enzymes as sensitive targets of anti-cancer drugs. Here we use one substrate–one intermediate–one final product model for a coupled enzyme system. The transfer rates for the mechanism are taken as continuous but subject to random fluctuations. Explicit formulae for the first moments of the distribution of the process are obtained. These formulae allow us to take into account not only the variability between the subjects, but also the variability of the process for a single subject. The present results allow us also to build the prediction interval for a particular time period given the observations for some preceding moments.     

Transmission,acute HIV-1 infection and the quest for strategies to prevent infection

By the acute stage of HIV-1 infection, the immune system already faces daunting challenges. Research on mucosal barriers and the events immediately after heterosexual transmission that precede this acute stage could facilitate the development of effective microbicides and vaccines.     

A Model for Mortality in a Self-thinning Plant Population

A model for mortality process in a self-thinning plant populationis proposed. It considers the spacial process but does not requirepositional information of each individual plant due to the assumptionsthat plants with interacting neighbours all greater than themselvesare the first to die and neighbours' sizes are mutually independentat each growth stage. Mortality of plants of size x at age t,M(t, x), is given as M(t, x) = m{P(t, x)}ⁿ where P(t, x) isthe proportion of plants of size greater than x at age t, andm and n are parameters. This model fits data from an experimentalplantation of Abies sachalinensis and will be useful for furtherdevelopment of the theoretical study of plant population growth. Abies sachalinensis Fr. Schm., self-thinning, mortality, size distribution, neighbourhood effect, spacial process model     

HIV-1 Autologous Antibody Neutralization Associates with Mother to Child Transmission

The HIV-1 characteristics associated with mother to child transmission (MTCT) are still poorly understood and if known would indicate where intervention strategies should be targeted. In contrast to horizontally infected individuals, exposed infants possess inherited antibodies (Abs) from their mother with the potential to protect against infection. We investigated the HIV-1 gp160 envelope proteins from seven transmitting mothers (TM) whose children were infected either during gestation or soon after delivery and from four non-transmitting mothers (NTM) with similar viral loads and CD4 counts. Using pseudo-typed viruses we tested gp160 envelope glycoproteins for TZM-bl infectivity, CD4 and CCR5 interactions, DC-SIGN capture and transfer and neutralization with an array of common neutralizing Abs (NAbs) (2F5, 2G12, 4E10 and b12) as well as mother and infant plasma. We found no viral correlates associated with HIV-1 MTCT nor did we find differences in neutralization with the panel of NAbs. We did, however, find that TM possessed significantly higher plasma neutralization capacities than NTM (P  = 0.002). Furthermore, we found that in utero (IU) TM had a higher neutralization capacity than mothers transmitting either peri - partum (PP) or via breastfeeding (BF) (P  = 0.002). Plasma from children infected IU neutralized viruses carrying autologous gp160 viral envelopes as well as those from their corresponding mothers whilst plasma from children infected PP and/or BF demonstrated poor neutralizing capacity. Our results demonstrate heightened autologous NAb responses against gp120/gp41 can associate with a greater risk of HIV-1 MTCT and more specifically in those infants infected IU. Although the number of HIV-1 transmitting pairs is low our results indicate that autologous NAb responses in mothers and infants do not protect against MTCT and may in fact be detrimental when considering IU HIV-1 transmissions.     

A Stochastic Model for Estimating Adolescent Sterility

In this article, a simple stochastic model for the time to first conception of a cohort of married women is developed, by identifying three states, ‘adolescent sterile’, ‘ovulating’ and ‘conceived‘, into which they can be placed. It is demonstrated that the model provides a close fit to observed data. The estimates of the parameters in the model, can be used to calculate the number of women in each state at different points of time and also to obtain estimates of the probabilities of conception for the two categories of women, adolescent sterile and biologically mature.     

The Combination of Phylogenetic Analysis with Epidemiological and Serological Data to Track HIV-1 Transmission in a Sexual Transmission Case

Objective

To investigate the linkage of HIV transmission from a man to a woman through unprotected sexual contact without disclosing his HIV-positive status.

Methods

Combined with epidemiological information and serological tests, phylogenetic analysis was used to test the a priori hypothesis of HIV transmission from the man to the woman. Control subjects, infected with HIV through heterosexual intercourse, from the same location were also sampled. Phylogenetic analyses were performed using the consensus gag, pol and env sequences obtained from blood samples of the man, the woman and the local control subjects. The env quasispecies of the man, the woman, and two controls were also obtained using single genome amplification and sequencing (SGA/S) to explore the paraphyletic relationship by phylogenetic analysis.

Results

Epidemiological information and serological tests indicated that the man was infected with HIV-1 earlier than the woman. Phylogenetic analyses of the consensus sequences showed a monophyletic cluster for the man and woman in all three genomic regions. Furthermore, gag sequences of the man and woman shared a unique recombination pattern from subtype B and C, which was different from those of CRF07_BC or CRF08_BC observed in the local samples. These indicated that the viral sequences from the two subjects display a high level of similarity. Further, viral quasispecies from the man exhibited a paraphyletic relationship with those from the woman in the Bayesian and maximum-likelihood (ML) phylogenetic trees of the env region, which supported the transmission direction from the man to the woman.

Conclusions

In the context of epidemiological and serological evidence, the results of phylogenetic analyses support the transmission from the man to the woman.