2,695 research outputs found
Speeding Up Network Simulations Using Discrete Time
We develop a way of simulating disease spread in networks faster at the cost
of some accuracy. Instead of a discrete event simulation (DES) we use a
discrete time simulation. This aggregates events into time periods. We prove a
bound on the accuracy attained. We also discuss the choice of step size and do
an analytical comparison of the computational costs. Our error bound concept
comes from the theory of numerical methods for SDEs and the basic proof
structure comes from the theory of numerical methods for ODEs
Bounds for the expected value of one-step processes
Mean-field models are often used to approximate Markov processes with large
state-spaces. One-step processes, also known as birth-death processes, are an
important class of such processes and are processes with state space
and where each transition is of size one. We derive explicit
bounds on the expected value of such a process, bracketing it between the
mean-field model and another simple ODE. Our bounds require that the Markov
transition rates are density dependent polynomials that satisfy a sign
condition. We illustrate the tightness of our bounds on the SIS epidemic
process and the voter model.Comment: 14 pages, 4 figures, revise
Modeling and controlling epidemic outbreaks: The role of population size, model heterogeneity and fast response in the case of measles
Modelers typically use detailed simulation models and vary the fraction vaccinated to study outbreak control. However, there is currently no guidance for modelers on how much detail (i.e., heterogeneity) is necessary and how large a population to simulate. We provide theoretical and numerical guidance for those decisions and also analyze the benefit of a faster public health response through a stochastic simulation model in the case of measles in the United States. Theoretically, we prove that the outbreak size converges as the simulation population increases and that the outbreaks are slightly larger with a heterogeneous community structure. We find that the simulated outbreak size is not sensitive to the size of the simulated population beyond a certain size. We also observe that in case of an outbreak, a faster public health response provides benefits similar to increased vaccination. Insights from this study can inform the control and elimination measures of the ongoing coronavirus disease (COVID-19) as measles has shown to have a similar structure to COVID-19
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