Parameter estimation for the stochastic SIS epidemic model
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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$100 (1-\alpha )\%$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>100</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mi mathvariant="italic">α</mi> <mo stretchy="false">)</mo> <mo>%</mo> </mrow> </math> </EquationSource> </InlineEquation> confidence intervals as well as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$100 (1-\alpha )\%$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>100</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mi mathvariant="italic">α</mi> <mo stretchy="false">)</mo> <mo>%</mo> </mrow> </math> </EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$100 (1-\alpha )\%$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>100</mn> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mi mathvariant="italic">α</mi> <mo stretchy="false">)</mo> <mo>%</mo> </mrow> </math> </EquationSource> </InlineEquation> joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory. Copyright Springer Science+Business Media Dordrecht 2014
