SEIR Model with All or Nothing Vaccination

Description

This example shows how to model an all or nothing vaccination intervenion on a SEIR epidemic over a dynamic network with vital dynamic processes for population entrance (e.g. birth) and exit (e.g. death).

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 SEIR modeling provides a general framework for transmission risk that is dependent on one's stage of disease progression. For more background on the SEIR model, see SEIR Model: Adding an Exposed State to an SIR.

The birth module implements a stochastic entrance process that acts as a function of a standard birth rate. The birth module has been modified to additionally simulate a stochastic all-or-nothing vaccination and vaccine protection processes. In an all-or-nothing vaccine model, the number who become vaccine protected is a product of the fraction vaccinated $\omega$ omega) and the fraction of the vaccinated who are protected by the vaccine $\chi$ (chi). Individuals who are conferred vaccine protection in an all-or-nothing model remain vaccine protected for the entirety of the model simulation - they are completely protected from infection and their degree of immunity does not wane. A key assumption of this particular all-or-nothing vaccination model is that individuals may not be vaccinated more than once. As a result, individuals who are vaccinated but are not conferred vaccine protection will not have the opportunity to become vaccine protected through subsequent vaccinations.

The death module implements a stochastic exit process that acts as a function of either a standard mortality rate or a disease-induced mortality rate.

Modules

The attribute initialization module (function = init_new_attrs) sets up the vaccine-related attribute values of nodes on the network. The starting population of individuals in the model may have received vaccination and may have vaccine protection as a result. Vaccination and vaccine protection rates can be user-defined by changing the vaccination.rate.initialization and protection.rate.initialization model parameters.

The death module (function = dfunc) simulates mortality as a function of disease-induced mortality. The module relies on the fact that a standard mortality rate is passed in by the module user as a rate - mortality.rate - in the epidemic model parameter settings. For those eligible (alive) individuals whose disease status is "i", the subsequent mortality rates are multiplied by the value of the mortality.disease.mult parameter.

The birth module (function = bfunc) has been extended from the birth model included in the github SEIR model example in order to include new logic around implementation of an all or nothing vaccine intervention. Vaccination and protection is simulated through two methods:

1. Progression - Unvaccinated individuals in the model have the opportunity to become vaccinated (e.g. through vaccination campaigns). However, only those individuals that receive vaccination when they are susceptible are considered vaccine protected. For each timestep in the model, vaccination of unvaccinated individuals is simulated followed by protection of those vaccinated individuals who are susceptible based on the vaccination.rate.progression and protection.rate.progression model parameters.
2. Birth - Individuals "born" into the population have the opportunity to become vaccinated (e.g. simulating the practice of vaccinating newborns). The vaccination may confer vaccine protection. Rates of vaccination and vaccine protection in individuals born into the network is determined by the vaccination.rate.births and protection.rate.births parameters.

Parameters

The epidemic model parameters include those needed for the SEIR model and those pertaining to vaccination and vaccine protection rates.

• inf.prob: the probability that an infection will occur given an act between a susceptible and infected node.
• act.rate the number of acts per partnership per unit time
• ei.rate the rate of exposed persons moving to the infectious state (1/average duration spent in E)
• ir.rate the rate of infectious persons moving to the recovered state (1/average duration spent in I)
• mortality.rate: a scalar for the standard mortality rate of the population. For disease status of "i", this rate is multiplied by the mortality.disease.mult explained below.
• mortality.disease.mult: the multiplier acting on mortality rate for persons with a disease status of "i".
• birth.rate: a scalar for the rate of births per person per week.
• vaccination.rate.initialization: A scalar for the proportion of the population at time 0 who are vaccinated.
• protection.rate.initialization: A scalar for the proportion of the population at time 0 who are confered vaccine protection after becoming vaccinated.
• vaccination.rate.progression: A scalar for the proportion of the unvaccinated population who become vaccinated throughout the simulation progression.
• protection.rate.progression: A scalar for the proportion of the susceptible and newly vaccinated population who become vaccinated through the vaccination progression method and who are confered vaccine protection.
• vaccination.rate.births: A scalar for the proportion of the individuals who enter into the network vaccinated.
• protection.rate.births: A scalar for the proportion of individuals who enter into the network vaccinated and are confered vaccine protection.

Authors

Connor M. Van Meter, Emory University