Christoforos Hadjichrysanthou

Evolutionary games on graphs and the speed of the evolutionary process

In this paper, we investigate evolutionary games with the invasion process updating rules on three simple non-directed graphs: the star, the circle and the complete graph. Here, we present an analytical approach and derive the exact solutions of the stochastic evolutionary game dynamics. We present formulae for the fixation probability and also for the speed of the evolutionary process, namely for the mean time to absorption (either mutant fixation or extinction) and then the mean time to mutant fixation. Through numerical examples, we compare the different impact of the population size and the fitness of each type of individual on the above quantities on the three different structures. We do this comparison in two specific cases. Firstly, we consider the case where mutants have fixed fitness r and resident individuals have fitness 1. Then, we consider the case where the fitness is not constant but depends on games played among the individuals, and we introduce a ‘hawk–dove’ game as an example.

Two results on evolutionary processes on general non-directed graphs

The paper [Broom & Rychtař (2008)][1] analytically investigated the probability for mutants to fixate in an otherwise uniform population on two types of heterogeneous graphs (lines and stars) by evolutionary dynamics. The main motivation for concentrating on those two types of graphs only was the

Evolutionary Games on Star Graphs Under Various Updating Rules

Evolutionary game dynamics have been traditionally studied in well-mixed populations where each individual is equally likely to interact with every other individual. Recent studies have shown that the outcome of the evolutionary process might be significantly affected if the population has a non-homogeneous structure. In this paper we study analytically an evolutionary game between two strategies interacting on an extreme heterogeneous graph, the star graph. We find explicit expressions for the fixation probability of mutants, and the time to absorption (elimination or fixation of mutants) and fixation (absorption conditional on fixation occurring). We investigate the evolutionary process considering four important update rules. For each of the update rules, we find appropriate conditions under which one strategy is favoured over the other. The process is considered in four different scenarios: the fixed fitness case, the Hawk–Dove game, the Prisoner’s dilemma and a coordination game. It is shown that in contrast with homogeneous populations, the choice of the update rule might be crucial for the evolution of a non-homogeneous population.

Why do so many clinical trials of therapies for Alzheimer's disease fail?

Alzheimer’s disease is an irreversible, progressive brain disorder that accounts for about 50–75% of all cases of dementia. Alzheimer’s disease is characterised by the presence of amyloid plaques (amyloid β) and neurofibrillary (tau) tangles, plus the loss of connections between neurons in the brain. The damage to the brain induced by abnormal deposits of amyloid β and tau tangles is believed to start a decade or more before a decline in cognitive function is apparent. Three stages in disease progression are commonly recognised: the preclinical stage without symptoms (cognitively normal), mild cognitive impairment, and the final stage of Alzheimer’s disease that is stratified into mild, moderate, and severe phases. To measure the stage of disease in patients, a focus of research is to define the relations between three groups of variables. These variables consist of scores in cognitive tests, concentrations of specific biomarker proteins (eg, tau and amyloid β) in cerebral spinal fluid, and brain scans to measure brain volume changes and protein deposition (MRI and PET scans), each of which might serve as an endpoint in the design of clinical trials of possible therapies. The Alzheimer’s Disease Assessment Scale-Cognition subscale (ADAS-Cog) is the most widely used general cognitive measure in clinical trials of Alzheimer’s disease. Research is focused on the development of therapies to delay or halt the progression of Alzheimer’s disease. However, no disease-modifying drug for Alzheimer’s disease has been approved, despite many long and expensive trials. A recent failure in phase 3 was β secretase (BACE) in patients with mild-to-moderate Alzheimer’s disease. Other large phase 3 trials of antiamyloid approaches with disappointing results include semagacestat, bapineuzumab, and solanezumab. Many explanations have been proposed for the failures of trials of disease-modifying drugs for Alzheimer’s disease, including starting the test of therapies too late in disease development, incorrect drug doses, wrong treatment target, and an inadequate understanding of the biology of Alzheimer’s disease. All may be true, but could there be a simpler explanation based on the choice of the clinical endpoint for the trials and associated variability in measurement of endpoints within or between individuals? The importance of this variability in all three groups of measurements—cognitive tests, biomarkers, and brain scans—can be tested with clinical trial simulators. Clinical trial simulators use computational approaches based on mathematical models of disease induction and progression to explore the potential outcomes of a clinical trial under various trial designs and endpoint choices. They are powerful tools for increasing understanding of how the pharmacokinetics and pharmacodynamics of a drug influence the choices of the clinical endpoint, sample size, patient recruitment criteria, and trial duration. For Alzheimer’s disease the mathematical model of disease progression can be based on the description of the probability (a transition probability) that a patient moves between healthy and diseased states (eg, from cognitively normal to mild cognitive impairment or from mild

A Systematic Review of Longitudinal Studies Which Measure Alzheimer’s Disease Biomarkers

Alzheimer’s disease (AD) is a progressive and fatal neurodegenerative disease, with no effective treatment or cure. A gold standard therapy would be treatment to slow or halt disease progression; however, knowledge of causation in the early stages of AD is very limited. In order to determine effective endpoints for possible therapies, a number of quantitative surrogate markers of disease progression have been suggested, including biochemical and imaging biomarkers. The dynamics of these various surrogate markers over time, particularly in relation to disease development, are, however, not well characterized. We reviewed the literature for studies that measured cerebrospinal fluid or plasma amyloid-β and tau, or took magnetic resonance image or fluorodeoxyglucose/Pittsburgh compound B-positron electron tomography scans, in longitudinal cohort studies. We summarized the properties of the major cohort studies in various countries, commonly used diagnosis methods and study designs. We have concluded that additional studies with repeat measures over time in a representative population cohort are needed to address the gap in knowledge of AD progression. Based on our analysis, we suggest directions in which research could move in order to advance our understanding of this complex disease, including repeat biomarker measurements, standardization and increased sample sizes.

Understanding the within-host dynamics of influenza A virus: from theory to clinical implications

Mathematical models have provided important insights into acute viral dynamics within individual patients. In this paper, we study the simplest target cell-limited models to investigate the within-host dynamics of influenza A virus infection in humans. Despite the biological simplicity of the models, we show how these can be used to understand the severity of the infection and the key attributes of possible immunotherapy and antiviral drugs for the treatment of infection at different times post infection. Through an analytic approach, we derive and estimate simple summary biological quantities that can provide novel insights into the infection dynamics and the definition of clinical endpoints. We focus on nine quantities, including the area under the viral load curve, peak viral load, the time to peak viral load and the level of cell death due to infection. Using Markov chain Monte Carlo methods, we fitted the models to data collected from 12 untreated volunteers who participated in two clinical studies that tested the antiviral drugs oseltamivir and zanamivir. Based on the results, we also discuss various difficulties in deriving precise estimates of the parameters, even in the very simple models considered, when experimental data are limited to viral load measures and/or there is a limited number of viral load measurements post infection.

Approximating evolutionary dynamics on networks using a neighbourhood configuration model

Evolutionary dynamics have been traditionally studied on homogeneously mixed and infinitely large populations. However, real populations are finite and characterised by complex interactions among individuals. Recent studies have shown that the outcome of the evolutionary process might be significantly affected by the population structure. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. In this paper, we adopt an approximation method which has been recently used for the modelling of infectious disease transmission to model evolutionary game dynamics on complex networks. Comparisons of the predictions of the model constructed with the results of computer simulations reveal the effectiveness of the method and the improved accuracy that it provides when, for example, compared to well-known pair approximation methods. This modelling framework offers a flexible way to carry out a systematic analysis of evolutionary game dynamics on graphs and to establish the link between network topology and potential system behaviours. As an example, we investigate how the Hawk and Dove strategies in a Hawk-Dove game spread in a population represented by a random regular graph, a random graph and a scale-free network, and we examine the features of the graph which affect the evolution of the population in this particular game.

Trends in the incidence of dementia: design and methods in the Alzheimer Cohorts Consortium.

Several studies have reported a decline in incidence of dementia which may have large implications for the projected burden of disease, and provide important guidance to preventive efforts. However, reports are conflicting or inconclusive with regard to the impact of gender and education with underlying causes of a presumed declining trend remaining largely unidentified. The Alzheimer Cohorts Consortium aggregates data from nine international population-based cohorts to determine changes in the incidence of dementia since 1990. We will employ Poisson regression models to calculate incidence rates in each cohort and Cox proportional hazard regression to compare 5-year cumulative hazards across study-specific epochs. Finally, we will meta-analyse changes per decade across cohorts, and repeat all analysis stratified by sex, education and APOE genotype. In all cohorts combined, there are data on almost 69,000 people at risk of dementia with the range of follow-up years between 2 and 27. The average age at baseline is similar across cohorts ranging between 72 and 77. Uniting a wide range of disease-specific and methodological expertise in research teams, the first analyses within the Alzheimer Cohorts Consortium are underway to tackle outstanding challenges in the assessment of time-trends in dementia occurrence.

Using Clinical Trial Simulators to Analyse the Sources of Variance in Clinical Trials of Novel Therapies for Acute Viral Infections.

Background About 90% of drugs fail in clinical development. The question is whether trials fail because of insufficient efficacy of the new treatment, or rather because of poor trial design that is unable to detect the true efficacy. The variance of the measured endpoints is a major, largely underestimated source of uncertainty in clinical trial design, particularly in acute viral infections. We use a clinical trial simulator to demonstrate how a thorough consideration of the variability inherent in clinical trials of novel therapies for acute viral infections can improve trial design. Methods and Findings We developed a clinical trial simulator to analyse the impact of three different types of variation on the outcome of a challenge study of influenza treatments for infected patients, including individual patient variability in the response to the drug, the variance of the measurement procedure, and the variance of the lower limit of quantification of endpoint measurements. In addition, we investigated the impact of protocol variation on clinical trial outcome. We found that the greatest source of variance was inter-individual variability in the natural course of infection. Running a larger phase II study can save up to

How Can Viral Dynamics Models Inform Endpoint Measures in Clinical Trials of Therapies for Acute Viral Infections

38 million, if an unlikely to succeed phase III trial is avoided. In addition, low-sensitivity viral load assays can lead to falsely negative trial outcomes. Conclusions Due to high inter-individual variability in natural infection, the most important variable in clinical trial design for challenge studies of potential novel influenza treatments is the number of participants. 100 participants are preferable over 50. Using more sensitive viral load assays increases the probability of a positive trial outcome, but may in some circumstances lead to false positive outcomes. Clinical trial simulations are powerful tools to identify the most important sources of variance in clinical trials and thereby help improve trial design.