Comparison of the Luus−Jaakola Optimization and Gauss−Newton Methods for Parameter Estimation in Ordinary Differential Equation Models

2006 ◽  
Vol 45 (13) ◽  
pp. 4716-4725 ◽  
Author(s):  
Praveen Linga ◽  
Nayef Al-Saifi ◽  
Peter Englezos
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parameter Estimation ◽  
Newton Methods ◽  
Differential Equation Models

Profile likelihood-based analyses of infectious disease models

2018 ◽  
Vol 27 (7) ◽  
pp. 1979-1998 ◽  
Author(s):  
Christian Tönsing ◽  
Jens Timmer ◽  
Clemens Kreutz
Keyword(s):  
Infectious Disease ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parameter Estimation ◽  
Profile Likelihood ◽  
Disease Models ◽  
Optimization Approach ◽  
Modeling Framework ◽  
Differential Equation Models ◽  
Infectious Disease Models

Ordinary differential equation models are frequently applied to describe the temporal evolution of epidemics. However, ordinary differential equation models are also utilized in other scientific fields. We summarize and transfer state-of-the art approaches from other fields like Systems Biology to infectious disease models. For this purpose, we use a simple SIR model with data from an influenza outbreak at an English boarding school in 1978 and a more complex model of a vector-borne disease with data from the Zika virus outbreak in Colombia in 2015–2016. Besides parameter estimation using a deterministic multistart optimization approach, a multitude of analyses based on the profile likelihood are presented comprising identifiability analysis and model reduction. The analyses were performed using the freely available modeling framework Data2Dynamics (data2dynamics.org) which has been awarded as best performing within the DREAM6 parameter estimation challenge and in the DREAM7 network reconstruction challenge.

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