Mathematical and Statistical Modeling in Complex Diseases

Dear Colleagues,

This special issue aims to showcase the critical role of mathematical and statistical modeling in advancing our understanding and treatment of complex diseases, including but not limited to dementia, cancer, cardiovascular disorders, and infectious diseases. These modeling frameworks support clinical decision-making, enable the design of optimized therapeutic strategies, and provide deep insights into disease mechanisms. We welcome both methodological advances and applied research utilizing real-world clinical or biological data.

1. Mathematical Modeling in Disease Research

Mathematical models serve as essential tools for decoding biological systems, forecasting disease progression, and evaluating treatment strategies across a wide spectrum of illnesses.

Mechanistic Modeling:

Differential equations (ordinary and partial) are widely used to describe the temporal and spatial dynamics of disease processes—for example, amyloid-beta aggregation in dementia, tumor growth and angiogenesis in cancer, and pathogen transmission in infectious diseases.

Stochastic models introduce biological variability, useful in simulating random mutations in cancer or heterogeneous progression in neurodegenerative disorders.

Network-based approaches model systems such as gene regulatory and neural networks, offering insights into disruptions caused by disease and helping to identify therapeutic targets.

Translational and Clinical Applications:

Mathematical models are increasingly used to optimize intervention strategies, including drug dosing and timing. For instance, pharmacokinetic/pharmacodynamic (PK/PD) models in oncology and simulations of disease-modifying therapies in dementia offer valuable preclinical insights.

Clinical trial simulations, especially in silico trials, enhance the efficiency of trial design by predicting outcomes and estimating statistical power—particularly crucial in precision medicine where patient variability is high.

Modeling of biomarker dynamics—such as tau and amyloid in dementia or circulating tumor DNA in cancer—facilitates early diagnosis and longitudinal monitoring.

2. Statistical Modeling in Clinical Studies

Statistical approaches provide robust tools to analyze clinical, observational, and high-dimensional datasets. These models are instrumental in risk assessment, early diagnosis, and understanding disease heterogeneity.

Predictive Modeling and Risk Stratification:

Techniques such as logistic regression, Cox models, and machine learning (e.g., neural networks, random forests) are applied to predict individual outcomes. In oncology, for example, integrating genomic and clinical data enhances personalized treatment strategies.

Modeling Progression and Heterogeneity:

Latent class models, hidden Markov models, and event-based frameworks are employed to capture complex, individualized disease trajectories—crucial in understanding multifactorial conditions like dementia or cancer.

3. Interdisciplinary Collaboration and Future Directions

The integration of mathematical and statistical modeling into medical research thrives on interdisciplinary collaboration among clinicians, biologists, data scientists, and computational modelers. This issue encourages submissions that reflect such collaboration and address innovative directions, such as AI-enhanced simulations, digital twins in healthcare, and ethical considerations in modeling patient data.

By bringing together diverse perspectives and methodologies, this special issue aims to foster advances that are both scientifically rigorous and clinically meaningful. We look forward to contributions that push the boundaries of what modeling can achieve in the realm of complex disease research.

Dr. Shantia Yarahmadian
Prof. Dr. Seth F. Oppenheimer
Guest Editors

Manuscript Submission Information

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• partial differential equations
• mathematical biology
• mathematical modeling
• complex diseases