7,529 research outputs found
Disease-induced resource constraints can trigger explosive epidemics
Advances in mathematical epidemiology have led to a better understanding of
the risks posed by epidemic spreading and informed strategies to contain
disease spread. However, a challenge that has been overlooked is that, as a
disease becomes more prevalent, it can limit the availability of the capital
needed to effectively treat those who have fallen ill. Here we use a simple
mathematical model to gain insight into the dynamics of an epidemic when the
recovery of sick individuals depends on the availability of healing resources
that are generated by the healthy population. We find that epidemics spiral out
of control into "explosive" spread if the cost of recovery is above a critical
cost. This can occur even when the disease would die out without the resource
constraint. The onset of explosive epidemics is very sudden, exhibiting a
discontinuous transition under very general assumptions. We find analytical
expressions for the critical cost and the size of the explosive jump in
infection levels in terms of the parameters that characterize the spreading
process. Our model and results apply beyond epidemics to contagion dynamics
that self-induce constraints on recovery, thereby amplifying the spreading
process.Comment: 24 pages, 6 figure
Epidemics on Networks: Reducing Disease Transmission Using Health Emergency Declarations and Peer Communication
Understanding individual decisions in a world where communications and
information move instantly via cell phones and the internet, contributes to the
development and implementation of policies aimed at stopping or ameliorating
the spread of diseases. In this manuscript, the role of official social network
perturbations generated by public health officials to slow down or stop a
disease outbreak are studied over distinct classes of static social networks.
The dynamics are stochastic in nature with individuals (nodes) being assigned
fixed levels of education or wealth. Nodes may change their epidemiological
status from susceptible, to infected and to recovered. Most importantly, it is
assumed that when the prevalence reaches a pre-determined threshold level, P*,
information, called awareness in our framework, starts to spread, a process
triggered by public health authorities. Information is assumed to spread over
the same static network and whether or not one becomes a temporary informer, is
a function of his/her level of education or wealth and epidemiological status.
Stochastic simulations show that threshold selection P* and the value of the
average basic reproduction number impact the final epidemic size
differentially. For the Erdos-Renyi and Small-world networks, an optimal choice
for P* that minimize the final epidemic size can be identified under some
conditions while for Scale-free networks this is not case
Equation-Free Multiscale Computational Analysis of Individual-Based Epidemic Dynamics on Networks
The surveillance, analysis and ultimately the efficient long-term prediction
and control of epidemic dynamics appear to be one of the major challenges
nowadays. Detailed atomistic mathematical models play an important role towards
this aim. In this work it is shown how one can exploit the Equation Free
approach and optimization methods such as Simulated Annealing to bridge
detailed individual-based epidemic simulation with coarse-grained,
systems-level, analysis. The methodology provides a systematic approach for
analyzing the parametric behavior of complex/ multi-scale epidemic simulators
much more efficiently than simply simulating forward in time. It is shown how
steady state and (if required) time-dependent computations, stability
computations, as well as continuation and numerical bifurcation analysis can be
performed in a straightforward manner. The approach is illustrated through a
simple individual-based epidemic model deploying on a random regular connected
graph. Using the individual-based microscopic simulator as a black box
coarse-grained timestepper and with the aid of Simulated Annealing I compute
the coarse-grained equilibrium bifurcation diagram and analyze the stability of
the stationary states sidestepping the necessity of obtaining explicit closures
at the macroscopic level under a pairwise representation perspective
Calculation of disease dynamics in a population of households
Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptible-infectious-recovered-suscep​tible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks
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