Revision as of 17:50, 21 July 2008

Introduction

STEM provides a way for users to input data from CSV Files and Estimated model parameters in, for example, an SIR or SEIR model so that model will best approximate the input data.

Mathematics

SI Models and Parameter Estimation

SIR Models and Parameter Estimation

SEIR Models and Parameter Estimation

There are four equations with four parameters that the SEIR model is defined by:

dS/dt = -βSI + αR

dE/dt = βSI - εE

dI/dt = εE - γI

dR/dt = γI - αR

where:

β is the infection rate

α is the immunity loss rate

γ is the infectious recovery rate

ε is the incubation rate

When rearranged by simple algebra, these four equations turn into the following:

(Eqn 1) (1/I)(dlnS/dt) = α (R/(SI)) - β

(Eqn 2) dlnE/dt = β (SI/E) - ε

(Eqn 3) dlnI/dt = ε (E/I) - γ

(Eqn 4) dlnR/dt = γ (I/R) - α

All four of the above equations are in the form y = mx + b, where:

(Eqn 1) x = R/(SI) and y = (1/I)(dlnS/dt)

(Eqn 2) x = SI/E and y = dlnE/dt

(Eqn 3) x = E/I and y = dlnI/dt

(Eqn 4) x = I/R and y = dlnR/dt

Using the method of least squares, we can fit all four equations to a line (y = mx + b) and get the slope (m) and intercept (b) from each equation. The slopes and interecepts in each equation corresponds to a parameter in the model equations.

Implementation

Package

All of the analysis is in the package org.eclipse.ohf.stem.analysis and projects within

Classes

ModelParamters.java