Abstract: Rapidly evaluating novel control measures against infectious diseases can be challenging, especially when the disease has a low incidence and it is characterized by a high degree of complexity. This is the case of invasive meningococcal diseases (IMD), rare but severe diseases hitting primarily infants, caused by bacteria asymptomatically carried by more than 10% of the general population, mostly among adolescents. A novel meningococcal vaccine, Bexsero, has been recently included for the first time in a national immunization programme, in the UK. This represents an unprecedented chance to evaluate such a vaccine. However, traditional statistical studies require large samples of observed disease cases to provide precise estimations. Thus, it may require several years of surveillance to precisely assess the effectiveness of Bexsero. We used a Monte Carlo Maximum Likelihood (MCML) approach to estimate both direct and indirect effectiveness of meningococcal vaccines. The method is based on stochastic simulations of an age-structured SIS model reproducing meningococcal transmission and vaccination. We calibrated the model to describe two immunization campaigns in the UK: the Bexsero campaign, started in the last fall, and a previous campaign, started in the 1999 and employing a different meningococcal vaccine, whose effectiveness has been already assessed using traditional studies. MCML estimates of vaccine effectiveness for the 1999 campaign are in good agreement with estimates from traditional studies, yet characterized by smaller confidence intervals. Also, we show that the MCML method could provide a fast and accurate estimate of the effectiveness of Bexsero, with a time gain that ranges from 2 to 15 years, depending on the value of effectiveness measured from field data. Our results show that inference methods based on dynamic computational models can be successfully used to quantify in near real-time the effectiveness of immunization campaigns, providing an important tool to complement and support traditional studies.

Abstract: Recent work has indicated that tropical forest and savanna can be alternative stable states under a range of climatic conditions. However, based on dynamical systems theory it may be expected that in case of strong spatial interactions between patches of alternative stable states, their coexistence becomes unstable. Boundaries between forest and savanna would then only be stable at conditions where the two states have equal potential, called the ‘Maxwell point’. Under different conditions, the state with the lowest potential would not be resilient against invasion of the state with highest potential. We used frequency distributions of MODIS tree-cover data at 250 m resolution to estimate Maxwell points with respect to the amount and seasonality of rainfall in both South America and Africa. We tested on a 0.5° scale whether there is a larger probability of local coexistence of forests and savannas near the estimated Maxwell points. Maxwell points for South America and Africa were estimated at 1760 mm and 1580 mm mean annual precipitation and at Markham’s Seasonality Index values of 50% and 24%. Although the probability of local coexistence was indeed highest around these Maxwell points, local coexistence was not limited to the Maxwell points. We conclude that critical transitions between forest and savanna may occur when climatic changes exceed a critical value. However, we also conclude that spatial interactions between patches of forest and savanna may reduce the hysteresis that can be observed in isolated patches, causing more predictable forest-savanna boundaries than continental-scale analyses of tree cover indicate. This effect could be less pronounced in Africa than in South America, where the forest-savanna boundary is substantially affected by rainfall seasonality.

Abstract: The main disabling factor of epilepsy is the sudden and usually unpredictable occurrence of seizures. However, seizures are not uniformly distributed in time. Periods of increased and decreased probability of seizure occurrence were observed in patients and in chronic models of epilepsy. Complex systems approaches helped to uncover power-law behaviour in distributions of seizure energy and inter-seizure intervals (ISI). The increase of the conditional waiting time until the next event with increasing the waiting time for the preceding event indicates a memory in the seizure dynamics. We have examined long-term seizure dynamics in the tetanus toxin model of temporal lobe epilepsy in eight adult rats. In all animals periods of high seizure frequency (clusters) were interspersed with periods of seizure absence or low seizure frequency. Concatenated data from all clusters confirm scale-free behaviour with the characteristic conditional waiting time behaviour. The study of individual clusters shows that seizures have a specific time-dependent dynamics. The clusters start with randomly occurring weaker seizures separated by short ISI’s which are followed by a progressive increase of ISI’s and seizure severity. In the present study we have concentrated on synchronization and information transfer in electrocorticographic signals in order to characterize the connectivity of epileptic networks in different parts of clusters, i.e. in seizures of different severity. An information-theoretic approach for detecting information transfer within and across different time scales, already successfully applied in a different multiscale complex system (M. Palus, Phys. Rev. Lett. 112(7), 078702, 2014) has been adapted for analysis of electrocorticograms. Understanding the mechanisms of the transition to seizures, and initiation and termination of seizure clusters can open new ways for the development of techniques for seizure forecasting and prevention. Support by the Czech Science Foundation (GACR 14-02634S) is gratefully acknowledged.

Abstract: The original form of the replicator equation was the first important tool to connect game dynamics, where individuals change their strategy over time, with evolutionary game theory, created by Maynard Smith and Price to predict the prevalence of competing strategies in evolving populations. The replicator equation was initially developed for infinitely large and well-mixed populations. Later, in 2006, using the standard pair approximation, H. Ohtsuki and M. Nowak proved that moving evolutionary game dynamics from a well-mixed population (a complete graph) onto a regular non-complete graph is simply described by a transformation of the payoff matrix. Under the assumption of weak selection, and using a new closure method for the pair approximation technique, we build a modified replicator equation on infinitely large graphs, for birth-death updating (a player is chosen with probability proportional to its fitness, and the offspring of this player replaces a random neighbour). The closure method that we propose takes into account the probability of triangles in the graph. Using this new equation, we study how graph structure can affect cooperation in some games with two different strategies, namely the Prisoner's Dilemma, the Snow-Drift Game and the Coordination Game. We compare our results with the ones that were obtained in the past using the standard replicator equation and the Ohtsuki-Nowak replicator equation on graphs. We also discuss how our modified pair approximation performs on different graphs, when compared to other approaches, and how it can be generalized, still satisfying the consistency conditions.

Abstract: The evolution is modeled by three main forces: genetic drift, mutation and selection. The most of complexity of biological life that arises from these simple operations is a result of their interplay. Not only different time scales characteristic to these mechanisms are responsible for the observed genetic variety, but also the diploid organization of the organisms that use sexual reproduction. This latter is a base for three kinds of selection: directional, underdominance and overdominance. Directional selection does not take advantage of diploid organization: its effect in diploid organisms is similar to that observed in haploid forms of life. Underdominance is a mechanism responsible for unstable allele frequency equilibrium and as such it is rarely observed in the nature. Some scientists consider it as a significant force leading to speciation. The third type, overdominance, is responsible for balancing selection because it results from stable allele frequency equilibrium. How strongly this genetic force may change genetic composition as compared with the neutral Kimura’s model shaped mostly by the genetic drift, is presented by the results of simulations using the author’s software. The outcomes of simulations are further compared with the predictions of the overdominance equilibrium model. The mechanism leading to observed interspecies polymorphism (for example the human-chimpanzee polymorphism detected in ATM gene by author’s earlier works) is explained based on results of simulated evolution in neutral and balancing selection models. Finally, the overwhelming complexity of contemporary life is considered in the light of serious bottlenecks for complexity present at the early life, such as complexity threshold and the limitation in the number of different genes before chromosomal organization of genome occurred. Significance of chromosomes as genetic information carriers further duplicated in diploid cells is concluded as a major architectural advantage required for the observed complexity of the life.