1,115 research outputs found
Threshold Dynamics of a Stochastic S
A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control
Optimal vaccination in a stochastic epidemic model of two non-interacting populations
Developing robust, quantitative methods to optimize resource allocations in
response to epidemics has the potential to save lives and minimize health care
costs. In this paper, we develop and apply a computationally efficient
algorithm that enables us to calculate the complete probability distribution
for the final epidemic size in a stochastic Susceptible-Infected-Recovered
(SIR) model. Based on these results, we determine the optimal allocations of a
limited quantity of vaccine between two non-interacting populations. We compare
the stochastic solution to results obtained for the traditional, deterministic
SIR model. For intermediate quantities of vaccine, the deterministic model is a
poor estimate of the optimal strategy for the more realistic, stochastic case.Comment: 21 pages, 7 figure
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
Suppressing disease spreading by using information diffusion on multiplex networks
Although there is always an interplay between the dynamics of information
diffusion and disease spreading, the empirical research on the systemic
coevolution mechanisms connecting these two spreading dynamics is still
lacking. Here we investigate the coevolution mechanisms and dynamics between
information and disease spreading by utilizing real data and a proposed
spreading model on multiplex network. Our empirical analysis finds asymmetrical
interactions between the information and disease spreading dynamics. Our
results obtained from both the theoretical framework and extensive stochastic
numerical simulations suggest that an information outbreak can be triggered in
a communication network by its own spreading dynamics or by a disease outbreak
on a contact network, but that the disease threshold is not affected by
information spreading. Our key finding is that there is an optimal information
transmission rate that markedly suppresses the disease spreading. We find that
the time evolution of the dynamics in the proposed model qualitatively agrees
with the real-world spreading processes at the optimal information transmission
rate.Comment: 11 pages, 8 figure
The dynamics of measles in sub-Saharan Africa.
Although vaccination has almost eliminated measles in parts of the world, the disease remains a major killer in some high birth rate countries of the Sahel. On the basis of measles dynamics for industrialized countries, high birth rate regions should experience regular annual epidemics. Here, however, we show that measles epidemics in Niger are highly episodic, particularly in the capital Niamey. Models demonstrate that this variability arises from powerful seasonality in transmission-generating high amplitude epidemics-within the chaotic domain of deterministic dynamics. In practice, this leads to frequent stochastic fadeouts, interspersed with irregular, large epidemics. A metapopulation model illustrates how increased vaccine coverage, but still below the local elimination threshold, could lead to increasingly variable major outbreaks in highly seasonally forced contexts. Such erratic dynamics emphasize the importance both of control strategies that address build-up of susceptible individuals and efforts to mitigate the impact of large outbreaks when they occur
Containing epidemic outbreaks by message-passing techniques
The problem of targeted network immunization can be defined as the one of
finding a subset of nodes in a network to immunize or vaccinate in order to
minimize a tradeoff between the cost of vaccination and the final (stationary)
expected infection under a given epidemic model. Although computing the
expected infection is a hard computational problem, simple and efficient
mean-field approximations have been put forward in the literature in recent
years. The optimization problem can be recast into a constrained one in which
the constraints enforce local mean-field equations describing the average
stationary state of the epidemic process. For a wide class of epidemic models,
including the susceptible-infected-removed and the
susceptible-infected-susceptible models, we define a message-passing approach
to network immunization that allows us to study the statistical properties of
epidemic outbreaks in the presence of immunized nodes as well as to find
(nearly) optimal immunization sets for a given choice of parameters and costs.
The algorithm scales linearly with the size of the graph and it can be made
efficient even on large networks. We compare its performance with topologically
based heuristics, greedy methods, and simulated annealing
Modeling the long term dynamics of pre-vaccination pertussis
The dynamics of strongly immunizing childhood infections is still not well
understood. Although reports of successful modeling of several incidence data
records can be found in the literature, the key determinants of the observed
temporal patterns have not been clearly identified. In particular, different
models of immunity waning and degree of protection applied to disease and
vaccine induced immunity have been debated in the literature on pertussis. Here
we study the effect of disease acquired immunity on the long term patterns of
pertussis prevalence. We compare five minimal models, all of which are
stochastic, seasonally forced, well-mixed models of infection based on
susceptible-infective-recovered dynamics in a closed population. These models
reflect different assumptions about the immune response of naive hosts, namely
total permanent immunity, immunity waning, immunity waning together with
immunity boosting, reinfection of recovered, and repeat infection after partial
immunity waning. The power spectra of the output prevalence time series
characterize the long term dynamics of the models. For epidemiological
parameters consistent with published data for pertussis, the power spectra show
quantitative and even qualitative differences that can be used to test their
assumptions by comparison with ensembles of several decades long
pre-vaccination data records. We illustrate this strategy on two publicly
available historical data sets.Comment: paper (31 pages, 11 figures, 1 table) and supplementary material (19
pages, 5 figures, 2 tables
- …