Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
نویسندگان
چکیده
In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase-planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor-pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed. The analysis offers insight into model behavior and suggests useful parameter regions, which simulations alone could not.
منابع مشابه
An efficient approach for availability analysis through fuzzy differential equations and particle swarm optimization
This article formulates a new technique for behavior analysis of systems through fuzzy Kolmogorov's differential equations and Particle Swarm Optimization. For handling the uncertainty in data, differential equations have been formulated by Markov modeling of system in fuzzy environment. First solution of these derived fuzzy Kolmogorov's differential equations has been found by Runge-Kutta four...
متن کاملMathematical Modeling of Cancer Cells and Chemotherapy Protocol Dealing Optimization Using Fuzzy Differential Equations And Lypunov Stability Criterion
Mathematical models can simulate the growth and proliferation of cells in the interaction with healthy cells, the immune system and measure the toxicity of drug and its effects on healthy tissue pay. One of the main goals of modeling the structure and growth of cancer cells is to find a control model suitable for administration among patients. In this study, a new mathematical model is designed...
متن کاملA case study of flood dynamic wave simulation in natural waterways using numerical solution of unsteady flows
Flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. Floods are taken unsteady flows that vary by time and location. Equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the Saint-Venant hypothesis is considered. Dynamic wave model as ...
متن کاملMathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...
متن کاملMathematical modeling and fuzzy availability analysis for serial processes in the crystallization system of a sugar plant
The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter enhances the uncertainty of the system reliability. In this paper, the concept of fuzzy reliability...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره 5 شماره
صفحات -
تاریخ انتشار 2016