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Mathematical models for the effects of hypertension and stress on kidney and their uncertainty

Tayebeh Waezizadeh1, Adel Mehrpooya2, Maryam Rezaeizadeh3

  • 1Department of Pure Mathematics, Faculty of Mathematics and Computer Shahid Bahonar University of Kerman, Kerman, 7616914111, Iran.

Mathematical Biosciences
|September 10, 2018
PubMed

Insights

Mathematical models predict Chronic Kidney Disease (CKD) progression. This study uses deterministic and stochastic approaches to analyze CKD, aiding in early detection and patient management.

Area of Science:

  • Nephrology
  • Mathematical Biology
  • Public Health

Background:

  • Chronic Kidney Disease (CKD) poses a significant public health challenge due to its progressive nature and potential for severe outcomes.
  • Hypertension and stress are identified as primary contributors to nephron damage, leading to reduced Glomerular Filtration Rate (GFR) and kidney dysfunction.

Purpose of the Study:

  • To develop and analyze mathematical models (deterministic and stochastic) for predicting Chronic Kidney Disease (CKD) progression.
  • To investigate the stability and stochastic stability of these models and address model uncertainty.

Main Methods:

  • Application of deterministic and stochastic mathematical modeling techniques to represent CKD.
  • Analysis of model equilibria, stability, and stochastic stability using mathematical theorems.
  • Utilizing MATLAB simulations to quantify uncertainty in stochastic models.

Main Results:

  • The study provides a comprehensive analysis of deterministic and stochastic models for CKD.
  • Mathematical theorems on model stability and stochastic stability are presented.
  • Simulations were performed to assess model uncertainty, and a predictive framework was developed.

Conclusions:

  • The developed mathematical models offer a framework for understanding and predicting CKD progression.
  • Validation with real clinical data supports the applicability of the models and theoretical findings.
  • This research contributes to better patient management and public health strategies for CKD.

Keywords:
Chronic kidney disease (CKD)EntropyStochastic modelingStochastic stability

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