scholarly journals Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

2016 ◽  
Vol 4 ◽  
Author(s):  
Marcus Rosenblatt ◽  
Jens Timmer ◽  
Daniel Kaschek
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parameter Estimation ◽  
Steady State ◽  
State Constraints ◽  
Linear Ordinary Differential Equation ◽  
Differential Equation Models ◽  
Non Linear

scholarly journals Initiation of thermal explosion by intense light: criticality dependence on data and parameters

1987 ◽  
Vol 28 (3) ◽  
pp. 287-295 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Steady State Solution ◽  
Linear Ordinary Differential Equation ◽  
Critical Parameters ◽  
Linear Parabolic Equation ◽  
Thermal Ignition ◽  
Non Linear ◽  
Intense Light

AbstractA model for thermal ignition by intense light is studied. The governing non-linear parabolic equation is linearized in a two-step manner with the aid of a non-linear ordinary differential equation which captures the salient features of the non-linear parabolic equation. The critical parameters are computed from the steady-state solution of the ordinary differential equation, which can be obtained without actually solving the equation. Comparison with available data shows that the present method yields good results.

scholarly journals Classroom Note: Numerical solutions of Nagumo's equation

1999 ◽  
Vol 3 (2) ◽  
pp. 189-193 ◽  
Author(s):  
M. Iqbal
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Solutions ◽  
Linear Ordinary Differential Equation ◽  
Bounded Solutions ◽  
Third Order ◽  
Non Linear

Nagumo's equation is a third order non-linear ordinary differential equation d3udx3−cd2udx2+f′(u)dudx−(b/c)u=0 where f(u)=u(1−u)(u−α) , 0<α<1 . In this paper we have developed a technique to determine those values of the parameters a,b and c which permit non-constant bounded solutions.

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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