EpiModel includes an integrated SIR model, but here we show how to model an SEIR disease like influenza. The E compartment in this disease is an exposed state in which a person has been infected but is not infectious to others. Many infectious diseases have this latent non-infectious stage, and in general it provides a general framework for transmission risk that is dependent on one’s stage of disease progression.
The built-in infection module (function = infect) is designed to handle a wide variety of specifications to the integrated network models. The main processes within the module are to extract a discordant edgelist, which is a matrix of ID numbers of active dyads in the network in which one member of the dyad is disease-susceptible and the other is infected. Given epidemic parameters for the probability of infection per act and the number of acts per unit time, the per-partnership transmission rate is calculated as an exponential function of the two. The key component that required updating in this module was to specify the newly infected person’s infection status as "e", whereas the default value transitions persons to "i".
The disease progression module (function = progress) will simulate the transition from exposed to infectious, and also the transition from infectious to recovered in the model. Instead both progression events are individual-level stochastic processes, in which there is a constant hazard of transition. The times spent in each disease compartment therefore follow a geometric distribution. The code block here is for the transition between exposed to infectious states. For each eligible person for transition, the event is modeled as a stochastic process following a Bernoulli distribution with the rate parameter, ei.rate. Persons who do transition to the infectious state have their individual-level status attribute updated to the "i" value, at which point they are now capable of infecting others.
The listing of main epidemic model parameters is as follows:
inf.probis the probability that an infection will occur given an act between a susceptible and infected nodeact.rateis the number of acts per partnership per unit timeei.rateis the rate of exposed persons moving to the infectious state (1/average duration spent inE)ir.rateis the rate of infectious persons moving to the recovered state (1/average duration spent inI)
In an extension contributed by Venkata R. Duvvuri, the SEIR model was expanded into an SEIRS model by adding an additional transition from the recovered state back into the susceptible state. The new parameter added:
rs.rateis the rate of recovered persons who loss their immunity after some time due to waning of immunity moving to the susceptible state (1/average duration spent inR)
Good next steps for this example might be to incorporate a vaccination or intervention strategy, or to vary the rate of disease progression based on an additional attribute of persons in the network.
Samuel M. Jenness, Emory University (http://samueljenness.org/) Venkata R. Duvvuri