scholarly journals Parameter Subset Selection in Differential Equation Models with Dead Time

2018 ◽  
Vol 51 (18) ◽  
pp. 661-666 ◽  
Author(s):  
A. Duong Vo ◽  
Aly Elraghy ◽  
Kim B. McAuley
Keyword(s):  
Differential Equation ◽  
Dead Time ◽  
Subset Selection ◽  
Differential Equation Models ◽  
Parameter Subset Selection

Overview of Gene Regulatory Network Inference Based on Differential Equation Models

2020 ◽  
Vol 21 (11) ◽  
pp. 1054-1059
Author(s):  
Bin Yang ◽  
Yuehui Chen
Keyword(s):  
Differential Equation ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Network Inference ◽  
New Drugs ◽  
Gene Regulatory Network Inference ◽  
Ode Models ◽  
Differential Equation Models ◽  
Linear Ode ◽  
Gene Regulatory

: Reconstruction of gene regulatory networks (GRN) plays an important role in understanding the complexity, functionality and pathways of biological systems, which could support the design of new drugs for diseases. Because differential equation models are flexible androbust, these models have been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates the differential equation models for reverse engineering gene regulatory networks. We introduce three kinds of differential equation models, including ordinary differential equation (ODE), time-delayed differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are utilized to search the optimal structures and parameters of differential equation models. This investigation could provide a comprehensive understanding of differential equation models, and lead to the discovery of novel differential equation models.

scholarly journals Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ahmed A. Mahmoud ◽  
Sarat C. Dass ◽  
Mohana S. Muthuvalu ◽  
Vijanth S. Asirvadam
Keyword(s):  
Differential Equation ◽  
Maximum Likelihood ◽  
Delay Differential Equation ◽  
Information Matrix ◽  
Likelihood Inference ◽  
Multiple Delays ◽  
Unknown Parameters ◽  
Differential Equation Models ◽  
Delay Differential ◽  
Initial Starting

This article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the trajectories of the delay differential equation models. The maximum likelihood estimator is obtained based on adaptive grid and Newton-Raphson algorithms. Our methodology estimates correctly the delay parameters as well as other unknown parameters (such as the initial starting values) of the dynamical system based on simulation data. We also develop methodology to compute the information matrix and confidence intervals for all unknown parameters based on the likelihood inferential framework. We present three illustrative examples related to biological systems. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2014b.

scholarly journals Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture

2021 ◽  
Author(s):  
Benjamin P Holder ◽  
Catherine A. A. Beauchemin
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Influenza Infection ◽  
Biologically Relevant ◽  
Differential Equation Models ◽  
Viral Yield ◽  
Infection Parameters ◽  
Delay Differential

Background For a typical influenza infection in vivo, viral titers over time are characterized by 1–2 days of exponential growth followed by an exponential decay. This simple dynamic can be reproduced by a broad range of mathematical models which makes model selection and the extraction of biologically-relevant infection parameters from experimental data difficult. Results We analyze in vitro experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of realistic models of infection. In particular, we demonstrate the viability of using a normal or lognormal distribution for the time a cell spends in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), while exposing the shortcomings of ordinary differential equation models which implicitly utilize exponential distributions and delay-differential equation models with fixed-length delays. Conclusions By fitting published viral titer data from challenge experiments in human volunteers, we show that alternative models can lead to different estimates of the key infection parameters.

scholarly journals Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 249
Author(s):  
Fasma Diele
Keyword(s):  
Differential Equation ◽  
Applied Mathematics ◽  
Special Issue ◽  
Differential Equation Models

The articles published in the Special Issue “Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges” of the MDPI Mathematics journal are here collected [...]

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