1 24-CompEpi

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1.1 High level overview of computational epidemiology


An example simulator

1.2 Code

1.2.1 Definitions

* The process starts by developing models of synthetic social contact networks and within host disease progression using diverse datasets that include: surveys, census, social media, serological investigations, and disease surveillance.
* High-performance computer simulations are then used to study the dynamics of disease propagation and the effects of various intervention strategies.
* The results are used by policymakers and analysts to formulate and evaluate various public policies as well as putative societal responses.
* All these models are refined, based on the simulation results and the policies being studied.

1.3 Historical

1.3.1 SIR model

24-CompEpi/sir_pop.png SIR over time


* The simplest aggregate model is popularly known as the SIR model.
* A population of size N is divided into three states: susceptible (S), infective (I), and removed or recovered (R).
* The following discrete time process describes the system dynamics:
* each infected person can infect any susceptible person (independently) with probability \(\beta\), and can recover with probability \(\gamma\).
* Let S(t), I(t) and R(t) denote the number of people who are susceptible, infected and recovered states at time t, respectively.
* Let:
\(s(t) = S(t)/N \\ i(t) = I(t)/N \\ r(t) = R(t)/N\)
\(s(t) + i(t) + r(t) = 1\)
By the “complete mixing” assumption that each individual is in contact with everyone in the population, it can be shown that the following system of differential equations (known as the SIR model) describes the dynamics:
\(\frac{ds(t)}{dt} = - \beta s(t) i(t) \\ \frac{di(t)}{dt} = \beta s(t) i(t) - \gamma i(t)\\ \frac{dr(t)}{dt} = \gamma i(t)\)
* One of the classic results in the SIR model is there is an epidemic that infects a large fraction of the population, if and only if \(R_0 = \beta / \gamma > 1\);
* The parameter \(R_0\) is known as the “reproductive number,” and thus much of public health decision making is centered on controlling \(R_0\). Similar models

24-CompEpi/sir.png Threshold


1.4 Modern

1.4.1 Networked epidemiology

a. Example showing a contact network on a population of size 6, represented by the set of nodes {v1, v2, v3, v4, v5, v6}.
b. An example of a dendogram on this contact graph, with the infected sets I(t), t = 0, 1, 2, 3 as shown.
* The teal edges represent the edges on which the infections spread.
* The infection starts at node v3, and eventually all nodes, except v1 get infected; the epicurve corresponding to this example is (1, 1, 2, 1), with the peak being at time 2.
c. Another possible dendogram on the same network, with the infection starting at v1, where all nodes except v2 get infected.

1.4.2 Process of generating a networked model

* Step 1. Construct a synthetic yet realistic population by integrating a variety of commercial and public sources.
* Step 2. Build a set of detailed activity templates for households using time-use surveys and digital traces. Assigns daily activities to individuals within a household using activity and time-use surveys as well as information available from social media.
* Step 3. Construct a dynamic social bipartite visitation network, GPL, which encodes the locations visited by each person. Constructs a dynamic social bipartite visitation network, represented by a (vertex and edge) labeled bipartite graph GPL, where P is the set of people and L is the set of locations.
* Step 4. Develop models of within-host disease progression using detailed case-based data and serological samples to establish disease parameters.
* Step 5. Develop high-performance computer simulations to study epidemic dynamics (exploring the Markov chain M).
* Step 6. Develop multi-theory multi-network models of individual, collective, and organizational behaviors, formulating and evaluating the efficacy of various intervention strategies and methods for situation assessment and epidemic forecasting. Step 1

Step 1:
* Construct a synthetic population statistically similar to census, by integrating a variety of commercial and public sources.
* We create synthetic urban populations by integrating a variety of databases from commercial and public sources into a common architecture for data exchange that preserves the confidentiality of the original data sets, and yet produces realistic attributes and demographics for the synthetic individuals.
* A census of our synthetic population yields results that are statistically indistinguishable from the original census data, if they are both aggregated to the block group level; this is illustrated in the schematic. Step 2

Step 2:
* Build a set of detailed activity templates for households based on activity and time-use surveys A set of activity templates for individuals in the households are determined, based on US census and survey data on activity and time-use surveys.
* These activity templates describe the sort of activities each household member performs and the time of day they are performed; a sample of such activity templates is shown. Step 3

Step 3:
* Construct a dynamic social bipartite visitation network, GPL, which encodes the locations visited by each person.
* The next step involves selecting locations where each of these activities are performed, for every person.
* Detailed statistical models developed in the transportation literature are used for this step; these are typically gravity models, which involve selecting locations based on a power of the distance.
* This is illustrated in the figure.

* The movement of people from one location to the next in their activity sequence is done by routing on the transportation network.
* By using a cellular automaton model for the actual movement, we get a very detailed spatio-temporal model of people.
* For the purpose of this paper, we use a bipartite graph representation of the this mobility, involving people and locations, as shown in the figure below. Step 5

* Models of disease progression are represented as probabilistic timed transition systems or PTTS, as shown in the figure.
* These are finite state systems with two additional features: transitions are triggered sometimes as a timed event and they can be probabilistic.
* In the example PTTS for a strain of flu in the figure below, an individual can transition to a latent state with probability 0.9 or to an incubating state with probability 0.1, if untreated; these probabilities change if the individual is vaccinated.
* If the person reaches a latent state, he switches to an infectious state in 2 days, during which time he can spread the infection to his uninfected and susceptible neighbors with some probability.
* Finally he switches to a recovered state in 3-5 days.
* The simulation of epidemic models on large populations involves evaluation over a network with a PTTS for every node.
* This is computationally very challenging, and we have developed four different simulation tools, that are relevant for different kinds of problems: EpiSims, EpiSimdemics, EpiFast and Indemics.
* Their performance is summarized in the table below.

1.4.3 Extensions of the basic model Timeline and Bayesian

24-CompEpi/bayes.png Other layers

* The layers represent examples of different kinds of networks in which the nodes might be involved.
* The bottom layer is a social contact network formed by co-location constraints, on which diseases spread.
* The middle layer is an information network, on which information/fear spread.
* Finally, the top layer is a friendship network that spreads influence, for example, peer pressure.

1.5 Data sources



Population density

Maps of disease-related activity (mosquitoes). Top species transmits Zika virus

Costs, benefits, and challenges of data sources