Stochastic SEIR Model

Overview

This app lets you explore a stochastic SEIR model. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

Learning Objectives

The Model

Model Overview

This model tracks susceptibles, exposed/pre-symptomatic, infected/symptomatic and recovered hosts. The following compartments are included:

The included processes/mechanisms are the following:

Model Implementation

The flow diagram for the model implemented in this app is:

Flow diagram for this model.

Flow diagram for this model.

Note that this model is not an ordinary differential equation model. It is instead its stochastic equivalent. We can specify the model by writing down every possible transition/event/reaction that can occur and their propensities (the propensity multiplied with the time step gives the probability that a given event/transition occurs). For our model these are the following:

Event type Transitions Propensity
Infection S => S-1, E => E+1 S(bEE+bII)
Progression to Symptoms E => E-1, I => I+1 gEE
Recovery I => I-1, R => R+1 gII
Waning of Immunity R => R-1, S => S+1 wR
Births S => S+1 m
Death of susceptible S => S-1 nS
Death of exposed E => E-1 nE
Death of symptomatic I => I-1 nI
Death of recovered R => R-1 nR

What to do

The tasks below are described in a way that assumes everything is in units of MONTHS (rate parameters, therefore, have units of inverse months). If any quantity is not given in those units, you need to convert it first (e.g. if it says a year, you need to convert it to 12 months).

Some of the simulations might take a few seconds to run. Be patient.

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Task 7:

Further Information

References

Black, F L. 1966. “Measles Endemicity in Insular Populations: Critical Community Size and Its Evolutionary Implication.” Journal of Theoretical Biology 11 (2): 207–11.

Keeling, M J. 1997. “Modelling the Persistence of Measles.” Trends in Microbiology 5 (12): 513–18. doi:10.1016/S0966-842X(97)01147-5.

Lloyd-Smith, James O, Paul C Cross, Cheryl J Briggs, Matt Daugherty, Wayne M Getz, John Latto, Maria S Sanchez, Adam B Smith, and Andrea Swei. 2005. “Should We Expect Population Thresholds for Wildlife Disease?” Trends in Ecology & Evolution 20 (9): 511–19. doi:10.1016/j.tree.2005.07.004.