45 research outputs found
Functional data learning using convolutional neural networks
In this paper, we show how convolutional neural networks (CNN) can be used in
regression and classification learning problems of noisy and non-noisy
functional data. The main idea is to transform the functional data into a 28 by
28 image. We use a specific but typical architecture of a convolutional neural
network to perform all the regression exercises of parameter estimation and
functional form classification. First, we use some functional case studies of
functional data with and without random noise to showcase the strength of the
new method. In particular, we use it to estimate exponential growth and decay
rates, the bandwidths of sine and cosine functions, and the magnitudes and
widths of curve peaks. We also use it to classify the monotonicity and
curvatures of functional data, algebraic versus exponential growth, and the
number of peaks of functional data. Second, we apply the same convolutional
neural networks to Lyapunov exponent estimation in noisy and non-noisy chaotic
data, in estimating rates of disease transmission from epidemic curves, and in
detecting the similarity of drug dissolution profiles. Finally, we apply the
method to real-life data to detect Parkinson's disease patients in a
classification problem. The method, although simple, shows high accuracy and is
promising for future use in engineering and medical applications.Comment: 38 pages, 23 figure
Multi-Type Branching Processes Modeling of Nosocomial Epidemics
Nosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number R0 and study its relationship with the parameters of the offspring distribution. in case of a single-type epidemic, we investigate the effect of contact tracing on the estimates for R0
Bounded rationality alters the dynamics of paediatric immunization acceptance
Interactions between disease dynamics and vaccinating behavior have been explored in many coupled behavior-disease models. Cognitive effects such as risk perception, framing, and subjective probabilities of adverse events can be important determinants of the vaccinating behaviour, and represent departures from the pure “rational” decision model that are often described as “bounded rationality”. However, the impact of such cognitive effects in the context of paediatric infectious disease vaccines has received relatively little attention. Here, we develop a disease-behavior model that accounts for bounded rationality through prospect theory. We analyze the model and compare its predictions to a reduced model that lacks bounded rationality. We find that, in general, introducing bounded rationality increases the dynamical richness of the model and makes it harder to eliminate a paediatric infectious disease. In contrast, in other cases, a low cost, highly efficacious vaccine can be refused, even when the rational decision model predicts acceptance. Injunctive social norms can prevent vaccine refusal, if vaccine acceptance is sufficiently high in the beginning of the vaccination campaign. Cognitive processes can have major impacts on the predictions of behaviourdisease models, and further study of such processes in the context of vaccination is thus warranted
Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical approach based on Monte Carlo integration to simulate solutions of fractional ordinary and partial differential equations. Thirdly, we show that this approach allows us to find the fundamental solutions for fractional partial differential equations (PDEs), in which the fractional derivative in time is in the Caputo sense and the fractional in space one is in the Riesz-Feller sense. Lastly, using Riccati equation, we study families of fractional PDEs with variable coefficients which allow explicit solutions. Those solutions connect Lie symmetries to fractional PDEs
The Influence Of Social Norms On The Dynamics Of Vaccinating Behaviour For Paediatric Infectious Diseases
Definitive version as published available at: Oraby, T., Thampi, V., & Bauch, C. T. (2014). The influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases. Proceedings of the Royal Society B: Biological Sciences, 281(1780), 20133172–20133172., http://dx.doi.org/10.1098/rspb.2013.3172Mathematical models that couple disease dynamics and vaccinating behaviour often assume that the incentive to vaccinate disappears if disease prevalence is zero. Hence, they predict that vaccine refusal should be the rule, and elimination should be difficult or impossible. In reality, countries with non-mandatory vaccination policies have usually been able to maintain elimination or very low incidence of paediatric infectious diseases for long periods of time. Here, we show that including injunctive social norms can reconcile such behaviour-incidence models to observations. Adding social norms to a coupled behaviour-incidence model enables the model to better explain pertussis vaccine uptake and disease dynamics in the UK from 1967 to 2010, in both the vaccine-scare years and the years of high vaccine coverage. The model also illustrates how a vaccine scare can perpetuate suboptimal vaccine coverage long after perceived risk has returned to baseline, pre-vaccine-scare levels. However, at other model parameter values, social norms can perpetuate depressed vaccine coverage during a vaccine scare well beyond the time when the population's baseline vaccine risk perception returns to pre-scare levels. Social norms can strongly suppress vaccine uptake despite frequent outbreaks, as observed in some small communities. Significant portions of the parameter space also exhibit bistability, meaning long-term outcomes depend on the initial conditions. Depending on the context, social norms can either support or hinder immunization goals
Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations
The work in this paper is four-fold. Firstly, we introduce an alternative
approach to solve fractional ordinary differential equations as an expected
value of a random time process. Using the latter, we present an interesting
numerical approach based on Monte Carlo integration to simulate solutions of
fractional ordinary and partial differential equations. Thirdly, we show that
this approach allows us to find the fundamental solutions for fractional
partial differential equations (PDEs), in which the fractional derivative in
time is in the Caputo sense and the fractional in space one is in the
Riesz-Feller sense. Lastly, using Riccati equation, we study families of
fractional PDEs with variable coefficients which allow explicit solutions.
Those solutions connect Lie symmetries to fractional PDEs.Comment: 23 pages, 5 figure