# Estimation of parameters for the SDE SIS epidemic model

Research output: Contribution to conferenceSpeech

### Abstract

In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and $100(1-\alpha)\%$ confidence intervals as well as $100(1-\alpha)\%$ joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic $100(1-\alpha)\%$ joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory.
Original language English Unpublished - 2012 Workshop on Stochastic Modelling in Ecosystems - Glasgow, United KingdomDuration: 11 Jun 2012 → 12 Jun 2012

### Conference

Conference Workshop on Stochastic Modelling in Ecosystems United Kingdom Glasgow 11/06/12 → 12/06/12

### Fingerprint

SIS Model
Confidence Region
Epidemic Model
Least Squares
Pseudo-maximum Likelihood
Least Squares Estimation
Maximum Likelihood Estimation
Confidence interval
Computer Simulation
Estimator
Estimate
Form

### Keywords

• Stochastic SIS epidemic model
• pseudo-maximum likelihood estimation
• least squares estimation
• confidence interval
• confidence region
• asymptotic estimator

### Cite this

Pan, J., Gray, A., Greenhalgh, D., & Mao, X. (2012). Estimation of parameters for the SDE SIS epidemic model. Workshop on Stochastic Modelling in Ecosystems, Glasgow, United Kingdom.
Pan, Jiafeng ; Gray, Alison ; Greenhalgh, David ; Mao, Xuerong. / Estimation of parameters for the SDE SIS epidemic model. Workshop on Stochastic Modelling in Ecosystems, Glasgow, United Kingdom.
@conference{264d47db644a4fcaa2909a8664064238,
title = "Estimation of parameters for the SDE SIS epidemic model",
abstract = "In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and $100(1-\alpha)\{\%}$ confidence intervals as well as $100(1-\alpha)\{\%}$ joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic $100(1-\alpha)\{\%}$ joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory.",
keywords = "Stochastic SIS epidemic model, pseudo-maximum likelihood estimation, least squares estimation, confidence interval, confidence region, asymptotic estimator",
author = "Jiafeng Pan and Alison Gray and David Greenhalgh and Xuerong Mao",
year = "2012",
language = "English",
note = "Workshop on Stochastic Modelling in Ecosystems ; Conference date: 11-06-2012 Through 12-06-2012",

}

Pan, J, Gray, A, Greenhalgh, D & Mao, X 2012, 'Estimation of parameters for the SDE SIS epidemic model', Workshop on Stochastic Modelling in Ecosystems, Glasgow, United Kingdom, 11/06/12 - 12/06/12.
2012. Workshop on Stochastic Modelling in Ecosystems, Glasgow, United Kingdom.

Research output: Contribution to conferenceSpeech

TY - CONF

T1 - Estimation of parameters for the SDE SIS epidemic model

AU - Pan, Jiafeng

AU - Gray, Alison

AU - Greenhalgh, David

AU - Mao, Xuerong

PY - 2012

Y1 - 2012

N2 - In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and $100(1-\alpha)\%$ confidence intervals as well as $100(1-\alpha)\%$ joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic $100(1-\alpha)\%$ joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory.

AB - In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and $100(1-\alpha)\%$ confidence intervals as well as $100(1-\alpha)\%$ joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic $100(1-\alpha)\%$ joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory.

KW - Stochastic SIS epidemic model

KW - pseudo-maximum likelihood estimation

KW - least squares estimation

KW - confidence interval

KW - confidence region

KW - asymptotic estimator

M3 - Speech

ER -

Pan J, Gray A, Greenhalgh D, Mao X. Estimation of parameters for the SDE SIS epidemic model. 2012. Workshop on Stochastic Modelling in Ecosystems, Glasgow, United Kingdom.