A Method for Reducing the Severity of Epidemics by Allocating Vaccines According to Centrality

One long-standing question in epidemiological research is how best to allocate limited amounts of vaccine or similar preventative measures in order to minimize the severity of an epidemic. Much of the literature on the problem of vaccine allocation has focused on influenza epidemics and used mathematical models of epidemic spread to determine the effectiveness of proposed methods. Our work applies computational models of epidemics to the problem of geographically allocating a limited number of vaccines within several Texas counties. We developed a graph-based, stochastic model for epidemics that is based on the SEIR model, and tested vaccine allocation methods based on multiple centrality measures. This approach provides an alternative method for addressing the vaccine allocation problem, which can be combined with more conventional approaches to yield more effective epidemic suppression strategies. We found that allocation methods based on in-degree and inverse betweenness centralities tended to be the most effective at containing epidemics.Comment: 10 pages, accepted to ACM BCB 201

Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page

A Mathematical Model to Study the Meningococcal Meningitis

AbstractThe main goal of this work is to introduce a novel mathematical model to study the spreading of meningococcal meningitis. Specifically, it is a discrete mathematical model based on cellular automata where the population is divided in five classes: sus- ceptible, asymptomatic infected, infected with symptoms, carriers, recovered and died. It catches the individual characteristics of people in order to give a prediction of both the individual behavior, and whole evolution of population

A Cellular Automata Modeling for Visualizing and Predicting Spreading Patterns of Dengue Fever

A Cellular Automata (CA) model is used for visualizing and predicting spreading pattern of the disease. The main problem of this model is how to find a function that represents an update rule that changes the state of a cell in time steps affected by neighborhood. This research aims to develop visualization and prediction model of the spreading patterns of Dengue Hemorrhagic Fever. The contribution of our study is to introduce a new approach in defining a probabilistic function that represents CA transmission rule by employing Von Neumann neighborhood and the Hidden Markov Model (HMM). This study only considered an infective state which dedicated particular attention to the spatial distribution of infected areas. The infected data were devided into four categories and change the definition of a cell as an area. The evaluation was conducted by comparing the results of the proposed model to that of one yielded by a Susceptible-Infected-Recovered (SIR) model. The evaluation result showed that the CA model was capable of generating patterns that similar to the patterns generated by SIR models with a similarities value of 0.95

A Simple Cellular Automaton Model for Influenza A Viral Infections

Viral kinetics have been extensively studied in the past through the use of spatially homogeneous ordinary differential equations describing the time evolution of the diseased state. However, spatial characteristics such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In order to investigate the influence of spatial heterogeneities on viral spread, a simple 2-D cellular automaton (CA) model of a viral infection has been developed. In this initial phase of the investigation, the CA model is validated against clinical immunological data for uncomplicated influenza A infections. Our results will be shown and discussed.Comment: LaTeX, 12 pages, 18 EPS figures, uses document class ReTeX4, and packages amsmath and SIunit

Invited review: Epidemics on social networks

Since its first formulations almost a century ago, mathematical models for disease spreading contributed to understand, evaluate and control the epidemic processes.They promoted a dramatic change in how epidemiologists thought of the propagation of infectious diseases.In the last decade, when the traditional epidemiological models seemed to be exhausted, new types of models were developed.These new models incorporated concepts from graph theory to describe and model the underlying social structure.Many of these works merely produced a more detailed extension of the previous results, but some others triggered a completely new paradigm in the mathematical study of epidemic processes. In this review, we will introduce the basic concepts of epidemiology, epidemic modeling and networks, to finally provide a brief description of the most relevant results in the field.Comment: 17 pages, 13 figure