Abstract:
Both pandemic and seasonal influenza are receiving more attention from mass media than ever before. Topics such as epidemic severity and vaccination are changing the way in which we perceive the utility of disease prevention. Voluntary influenza vaccination has been recently modeled using inductive reasoning games. It has thus been found that severe epidemics may occur because individuals do not vaccinate and, instead, attempt to benefit from the immunity of their peers. Such epidemics could be prevented by voluntary vaccination if incentives were offered. However, a key assumption has been that individuals make vaccination decisions based on whether there was an epidemic each influenza season; no other epidemiological information is available to them. In this work, we relax this assumption and investigate the consequences of making more informed vaccination decisions while no incentives are offered. We obtain three major results. First, individuals will not cooperate enough to constantly prevent influenza epidemics through voluntary vaccination no matter how much they learned about influenza epidemiology. Second, broadcasting epidemiological information richer than whether an epidemic occurred may stabilize the vaccination coverage and suppress severe influenza epidemics. Third, the stable vaccination coverage follows the trend of the perceived benefit of vaccination. However, increasing the amount of epidemiological information released to the public may either increase or decrease the perceived benefit of vaccination. We discuss three scenarios where individuals know, in addition to whether there was an epidemic, (i) the incidence, (ii) the vaccination coverage and (iii) both the incidence and the vaccination coverage, every influenza season. We show that broadcasting both the incidence and the vaccination coverage could yield either better or worse vaccination coverage than broadcasting each piece of information on its own.

Abstract:
We consider a five dimensional (5D) space-time with a space-like fifth dimension. We implement a quantum formalism by path integrals, and postulate that all the physical information on a 5D massless particle propagation is provided by the statistics over null paths in this 5D space-time. If the 5D metric is independent of the fifth coordinate, then the propagation problem can be reduced to four dimensions by foliation along the fifth coordinate, and we obtain a formulation of 4D Quantum Mechanics. If the 5D metric is independent of time, we foliate along the time coordinate, and obtain a formulation of 4D Statistical Mechanics. If the 5D metric is independent of both time and the fifth coordinate, then Quantum and Statistical Mechanics are pictures of the same 5D reality. We also discuss the foliation of a proper space dimension, the Klein-Gordon equation, and a 5D Special Relativity, completing our interpretation of the 5D geometry.

Abstract:
Pilot studies of structured treatment interruptions (STI) in HIV therapy have shown that patients can maintain low viral loads whilst benefiting from reduced treatment toxicity. However, a recent STI clinical trial reported a high degree of virologic failure. Here we present a novel hypothesis that could explain virologic failure to STI and provides new insights of great clinical relevance. We analyze a classic mathematical model of HIV within-host viral dynamics and find that nonlinear parametric resonance occurs when STI are added to the model; resonance is observed as virologic failure. We use the model to simulate clinical trial data and to calculate patient-specific resonant spectra. We gain two important insights. Firstly, within an STI trial, we determine that patients who begin with similar viral loads can be expected to show extremely different virologic responses as a result of resonance. Thus, high heterogeneity of patient response within a STI clinical trial is to be expected. Secondly and more importantly, we determine that virologic failure is not simply due to STI or patient characteristics; rather it is the result of a complex dynamic interaction between STI and patient viral dynamics. Hence, our analyses demonstrate that no universal regimen with periodic interruptions will be effective for all patients. On the basis of our results, we suggest that immunologic and virologic parameters should be used to design patient-specific STI regimens.

Abstract:
Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by the presence of chaotic saddles whose stable sets have fractal dimensions that are close to phase-space dimension. For many physical systems chaotic saddles have a big impact on laboratory measurements, and it is important to compute the dimension of such stable sets including fractal basin boundaries through a direct method. In this work, we present a new method to compute the dimension of stable sets of chaotic saddles directly, fast, and reliable.

Abstract:
Previous modeling studies have identified the vaccination coverage level necessary for preventing influenza epidemics, but have not shown whether this critical coverage can be reached. Here we use computational modeling to determine, for the first time, whether the critical coverage for influenza can be achieved by voluntary vaccination. We construct a novel individual-level model of human cognition and behavior; individuals are characterized by two biological attributes (memory and adaptability) that they use when making vaccination decisions. We couple this model with a population-level model of influenza that includes vaccination dynamics. The coupled models allow individual-level decisions to influence influenza epidemiology and, conversely, influenza epidemiology to influence individual-level decisions. By including the effects of adaptive decision-making within an epidemic model, we can reproduce two essential characteristics of influenza epidemiology: annual variation in epidemic severity and sporadic occurrence of severe epidemics. We suggest that individual-level adaptive decision-making may be an important (previously overlooked) causal factor in driving influenza epidemiology. We find that severe epidemics cannot be prevented unless vaccination programs offer incentives. Frequency of severe epidemics could be reduced if programs provide, as an incentive to be vaccinated, several years of free vaccines to individuals who pay for one year of vaccination. Magnitude of epidemic amelioration will be determined by the number of years of free vaccination, an individuals' adaptability in decision-making, and their memory. This type of incentive program could control epidemics if individuals are very adaptable and have long-term memories. However, incentive-based programs that provide free vaccination for families could increase the frequency of severe epidemics. We conclude that incentive-based vaccination programs are necessary to control influenza, but some may be detrimental. Surprisingly, we find that individuals' memories and flexibility in adaptive decision-making can be extremely important factors in determining the success of influenza vaccination programs. Finally, we discuss the implication of our results for controlling pandemics.

Abstract:
To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R0, is generally calculated from a population-level model. R0 specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R0 is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control. Conventionally, it is assumed that if R0>1 the outbreak generates an epidemic, and if R0<1 the outbreak becomes extinct. Here, we use computational and analytical methods to calculate the average number of secondary infections and to show that it does not necessarily represent an epidemic threshold parameter (as it has been generally assumed). Previously we have constructed a new type of individual-level model (ILM) and linked it with a population-level model. Our ILM generates the same temporal incidence and prevalence patterns as the population-level model; we use our ILM to directly calculate the average number of secondary infections (i.e., R0). Surprisingly, we find that this value of R0 calculated from the ILM is very different from the epidemic threshold calculated from the population-level model. This occurs because many different individual-level processes can generate the same incidence and prevalence patterns. We show that obtaining R0 from empirical contact tracing data collected by epidemiologists and using this R0 as a threshold parameter for a population-level model could produce extremely misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control.

Abstract:
To predict the impact of universal long-term flu vaccines on influenza epidemics we developed a mathematical model that linked human cognition and memory with the transmission dynamics of influenza. Our modeling shows that universal vaccines that provide short-term protection are likely to result in small frequent epidemics, whereas universal vaccines that provide long-term protection are likely to result in severe infrequent epidemics.Influenza vaccines that provide short-term protection maintain risk awareness regarding influenza in the population and result in stable vaccination coverage. Vaccines that provide long-term protection could lead to substantial drops in vaccination coverage and should therefore include an annual epidemic risk awareness programs in order to minimize the risk of severe epidemics.Influenza is the lead cause of death from a vaccine-preventable disease in the United States (US). Although about 80% of the US population is specifically recommended for annual influenza vaccination, less than 40% of the population usually gets vaccinated [1]. Despite the rising vaccination rates in recent years, these still fall short of Healthy People 2010 objectives [2,3]. Hopes are that the introduction of a new vaccine offering long-term protection over many years would lead to a significantly increase in the vaccination coverage. Recently, the possibility of developing such universal flu vaccines has become more tangible than ever before [4,5]. In early 2008, Acambis of Cambridge, Massachusetts (now Sanofi Pasteur) reported positive results for a phase 1 clinical trial of a universal vaccine [6]. Independently that same year, a group at Oxford, England, led by Dr. Gilbert started a phase 1 clinical trial of another universal flu vaccine that would provide protection for at least 5-10 years after which a booster will be required [7]. More recently, lab-made proteins have been identified which would allow the vaccine to neutralize a broad range of influenza

Abstract:
We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to be indeterminate in the sense that it is difficult to predict the eventual fate of an orbit that tracks the pre-bifurcation node attractor as the system parameter is swept through the bifurcation. In this paper we investigate the scaling of (1) the fractal basin boundary of the static (i.e., unswept) system near the saddle-node bifurcation, (2) the dependence of the orbit's final destination on the sweeping rate, (3) the dependence of the time it takes for an attractor to capture a swept orbit on the sweeping rate, and (4) the dependence of the final attractor capture probability on the noise level. With respect to noise, our main result is that the effect of noise scales with the 5/6 power of the parameter drift rate. Our approach is to first investigate all these issues using one-dimensional map models. The simplification of treatment inherent in one dimension greatly facilitates analysis and numerical experiment, aiding us in obtaining the new results listed above. Following our one-dimensional investigations, we explain that these results can be applied to two-dimensional systems. We show, through numerical experiments on a periodically forced second order differential equation example, that the scalings we have found also apply to systems that result in two dimensional maps.

Abstract:
Goods, styles, ideologies are adopted by society through various mechanisms. In particular, adoption driven by innovation is extensively studied by marketing economics. Mathematical models are currently used to forecast the sales of innovative goods. Inspired by the theory of diffusion processes developed for marketing economics, we propose, for the first time, a predictive framework for the mechanism of fashion, which we apply to first names. Analyses of French, Dutch and US national databases validate our modelling approach for thousands of first names, covering, on average, more than 50% of the yearly incidence in each database. In these cases, it is thus possible to forecast how popular the first names will become and when they will run out of fashion. Furthermore, we uncover a clear distinction between popularity and fashion: less popular names, typically not included in studies of fashion, may be driven by fashion, as well.

Abstract:
Inspired by Minority Games, we constructed a novel individual-level game of adaptive decision-making based on the dilemma of deciding whether to participate in voluntary influenza vaccination programs. The proportion of the population vaccinated (i.e., the vaccination coverage) determines epidemic severity. Above a critical vaccination coverage, epidemics are prevented; hence individuals find it unnecessary to vaccinate. The adaptive dynamics of the decisions directly affect influenza epidemiology and, conversely, influenza epidemiology strongly influences decision-making. This feedback mechanism creates a unique self-organized state where epidemics are prevented. This state is attracting, but unstable; thus epidemics are rarely prevented. This result implies that vaccination will have to be mandatory if the public health objective is to prevent influenza epidemics. We investigated how collective behavior changes when public health programs are implemented. Surprisingly, programs requiring advance payment for several years of vaccination prevents severe epidemics, even with voluntary vaccination. Prevention is determined by the individuals' adaptability, memory, and number of pre-paid vaccinations. Notably, vaccinating families exacerbates and increases the frequency of severe epidemics.