Nico Stollenwerk

The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis.

In many countries in Asia and South-America dengue fever (DF) and dengue hemorrhagic fever (DHF) has become a substantial public health concern leading to serious social-economic costs. Mathematical models describing the transmission of dengue viruses have focussed on the so-called antibody-dependent enhancement (ADE) effect and temporary cross-immunity trying to explain the irregular behavior of dengue epidemics by analyzing available data. However, no systematic investigation of the possible dynamical structures has been performed so far. Our study focuses on a seasonally forced (non-autonomous) model with temporary cross-immunity and possible secondary infection, motivated by dengue fever epidemiology. The notion of at least two different strains is needed in a minimalistic model to describe differences between primary infections, often asymptomatic, and secondary infection, associated with the severe form of the disease. We extend the previously studied non-seasonal (autonomous) model by adding seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of dengue fever epidemics. A comparative study between three different scenarios (non-seasonal, low seasonal and high seasonal with a low import of infected individuals) is performed. The extended models show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. We discuss the role of seasonal forcing and the import of infected individuals in such systems, the biological relevance and its implications for the analysis of the available dengue data. At the moment only such minimalistic models have a chance to be qualitatively understood well and eventually tested against existing data. The simplicity of the model (low number of parameters and state variables) offer a promising perspective on parameter values inference from the DHF case notifications.

The Impact of the Newly Licensed Dengue Vaccine in Endemic Countries

Background With approximately 3 billion people at risk of acquiring the infection, dengue fever is now considered the most important mosquito-borne viral disease in the world, with 390 million dengue infections occurring every year, of which 96 million manifest symptoms with any level of disease severity. Treatment of uncomplicated dengue cases is only supportive and severe dengue cases require hospital intensive care. A vaccine now licensed in several countries and developed by Sanofi Pasteur (CYD-TDV, named Dengvaxia), was able to protect, in the first 25 months of the two Phase III, 66% of a subset of 9–16 year old participants. However, a significantly lower efficacy (including negative vaccine efficacy) was noted for children younger than 9 years of age. Methodology/Principal Findings Analysis of year 3 results of phase III trials of Dengvaxia suggest high rates of protection of vaccinated partial dengue immunes but high rates of hospitalizations during breakthrough dengue infections of persons who were vaccinated when seronegative, with vaccine appearing to induce enhancing antibodies (ADE). An age structured model was developed based on Sanofi’s recommendation to vaccinate persons age 945 years in dengue endemic countries. The model was used to explore the clinical burden of two vaccination strategies: 1) Vaccinate 4 or 20% of individuals, ages 9–45 years, seropositives and seronegatives, and 2) vaccinate 4 or 20% of individuals, ages 9–45 years, who are dengue immune only. Conclusions/Significance Our results show that vaccinating dengue monotypic immune individuals prevents dengue hospitalizations, but at the same time dengue infections of vaccine-sensitized persons increases hospitalizations. When the vaccine is given only to partial immune individuals, after immunological screening of the population, disease burden decreases considerably.

Dynamic noise, chaos and parameter estimation in population biology

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models such as multi-strain dynamics to describe the virus–host interaction in dengue fever, even the most recently developed parameter estimation techniques, such as maximum likelihood iterated filtering, reach their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and the deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

Meningitis, pathogenicity near criticality:the epidemiology of meningococcal disease as a model for accidental pathogens

We formulate and analyse a model for infectious diseases transmitted by asymptomatic carriers finding, that if harmless and pathogenic strains of the infected agent compete, frequent outbreaks of the pathogenic strains can occur. A counterintuitively high number of clustered outbreaks at low pathogenicity in our model compares well with observations in diseases with severe and often fatal results for the host, as for example in meningitis. These clustered outbreaks can be described by the typical scaling behaviour around criticality. The epidemic model is a susceptible-infected-recovered system (SIR) for the harmless infective agent, acting as a background to a mutant strain Y which occasionally creates severely affected hosts X. The full system of SIRYX is described in the master equation framework, confirming limiting assumptions about a reduced YX-system with the SIR-system in stationarity. In this limiting case we can analytically show convergence to power law scaling typical for critical states, as well as the divergence of the variance of outbreaks near criticality. These large fluctuations of outbreaks of accidental pathogens as mutants of otherwise harmless commensal organisms is the challenging new feature of our model for future epidemiology of diseases like meningococcal disease.

Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ade and temporary cross immunity.

We analyse an epidemiological model of competing strains of pathogens and hence differences in transmission for first versus secondary infection due to interaction of the strains with previously aquired immunities, as has been described for dengue fever, is known as antibody dependent enhancement (ADE). These models show a rich variety of dynamics through bifurcations up to deterministic chaos. Including temporary cross-immunity even enlarges the parameter range of such chaotic attractors, and also gives rise to various coexisting attractors, which are difficult to identify by standard numerical bifurcation programs using continuation methods. A combination of techniques, including classical bifurcation plots and Lyapunov exponent spectra, has to be applied in comparison to get further insight into such dynamical structures. Here we present for the first time multi-parameter studies in a range of biologically plausible values for dengue. The multi-strain interaction with the immune system is expected to have implications for the epidemiology of other diseases also.

Bursting as a source for predictability in biological neural network activity

Abstract The role of bursting as a unit of neural information has received considerable support in the recent years. Experimental evidence shows that in many different neural systems, e.g. visual cortex or hippocampus, bursting is essential for coding and processing. We have recently demonstrated (Menendez de la Prida et al., 1996) the spontaneous presence of bursts in in vitro hippocampal slices from newborn animals, providing a good system to investigate bursting dynamics in physiological conditions. Here we analyze the interspike intervals (ISIs) of five intracellularly recorded cells from immature hippocampal networks. First, we test the time series against Poisson processes, typical of pure random behavior, using the Kolmogorov-Smirnov test. Only 2 5 records strongly deviate from Poisson process. Nonlinear diction tests are then applied to compare original series with its Gaussian-scaled random phase surrogates and signs of short time predictability are observed ( 1 5 ). This predictability is originated by the intrinsic structure of bursts, in an otherwise purely random process, and can be removed completely by eliminating the bursts from the original time series. Here we introduce this method of eliminating bursts to get insight into the nonlinear dynamics of firing. Also the interburst intervals are indistinguishable from pure noise. The analysis of unstable periodicities within the bursts in the original ISIs shows that signs of nonlinearities can be statistically differentiated from their surrogate realizations (Pierson-Moss method). We discuss the computational implication of these results.

The risks behind Dengvaxia recommendation

882 www.thelancet.com/infection Vol 16 August 2016 3 Capeding MR, Tran NH, Hadinegoro SRS, et al. Clinical effi cacy and safety of a novel tetravalent dengue vaccine in healthy children in Asia: a phase 3, randomised, observer-masked, placebo-controlled trial. Lancet 2014; 384: 1358–65. 4 Villar L, Dayan GH, Arredondo-García JL, et al. Effi cacy of a tetravalent dengue vaccine in children in Latin America. N Engl J Med 2014; 372: 113–23. 5 Wilder-Smith A, Gubler D. Dengue vaccines at a crossroads. Science 2015; 350: 626–27. 1 WHO. Global Strategy for Dengue Prevention and Control. 2012–2020. Geneva: World Health Organization, 2012. http://apps.who.int/iris/ bitstream/10665/75303/1/9789241504034_eng.pdf?ua=1 (accessed April 20, 2016). 2 WHO. Summary of the April 2016 meeting of the Strategic Advisory Group of Experts on immunization (SAGE). Geneva: World Health Organization, 2016. http://www.who.int/immunization/sage/ meetings/2016/april/SAGE_April_2016_Meeting_Web_summary. pdf?ua=1 (accessed April 20, 2016).

Scale-free network of a dengue epidemic

Abstract In this work we show that the dengue epidemic in the city of Singapore organized itself into a scale-free network of transmission as the 2000–2005 outbreaks progressed. This scale-free network of cluster comprised geographical breeding places for the aedes mosquitoes, acting as super-spreaders nodes in a network of transmission. The geographical organization of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our hypothesis is that the distribution of dengue cases reflects the geographical organization of a transmission network, which evolved towards a power law as the epidemic intensity progressed until 2005.

Nonlinear time series analysis of empirical population dynamics

The classical approach towards time series analysis of fluctuating phenomena is based on linear stochastic processes in the basin of attraction of globally stable equilibria (ARMA models). However, there are deductive reasons derived from nonequilibrium statistical mechanics that many self-generated population fluctuations should be interpreted as stochastic processes influenced by nonequilibrium attractors of nonlinear dynamical systems. The incidence pattern of measles epidemics in New York City is used to demonstrate that highly nonlinear autoregressive models can serve as a new semi-phenomenological level of description for complex self-generated fluctuations in biological or ecological systems. The nature of the unpredictability of the incidence pattern of measles is characterized by a subtle interaction between a chaotic nonlinear determinism and stochastic fluctuations. The sensitive dependence on initial conditions, characteristic for chaos, is not limited to chaotic attractors but can also occur on so-called chaotic transients. The dynamics of recurrent outbreaks of measles in New York City turns out to be close to a so-called boundary crisis which converts a stable chaotic attractor to metastable chaotic transients leading finally to a period-3 attractor. However, the demographic noise destabilizes the periodic orbit as well, and creates a situation of intermittent jumps between episodic periodicities and longer chaotic transients. A simple autoregressive model is used to achieve a plausible geometric understanding of the noise-induced intermittency switching between episodic periodicity and transient chaos.

Carnival or football, is there a real risk for acquiring dengue fever in Brazil during holidays seasons?

More than 600,000 football fans, coming from all over the world, were expected to visit Brazil during the FIFA World Cup 2014. International travel can become a public health problem when the visitors start to become sick, needing medical intervention and eventually hospitalization. The occurrence of dengue fever infections in Brazil is persistent and has been increasing since the 1980s, and the health authorities were expected to take preventive measures and to warn the visitors about the risks during the tournament period. Before the World Cup started, studies have been published stating that dengue could be a significant problem in some of the Brazilian cities hosting the games. These conclusions were taken after a brief observation of the available data, analyzing its mean and standard deviation only, or based on seasonal climate forecasts, causing alarm for the world cup in Brazil. Here, with a more careful data analysis, we show that the seasonality of the disease plays a major role in dengue transmission. The density of dengue cases in Brazil is residual during winter in the Southern hemisphere (mid June to mid September) and the fans of football were not likely to get dengue during the tournament period.