Epidemic models using optimal control theory

HIV/AIDS modeling

Heart dynamic modelling

Introduction

• Diastole is when the heart is in rest;
• Systole is when the heart is contracted;
• The heart just has the ability to push out, not suck in. 

Mathematical modeling of the glucose–insulin system

Palumbo P, Ditlevsen S, Bertuzzi A, De Gaetano A, Mathematical modeling of the glucose–insulin system: A review, Mathematical Biosciences 244 (2013) 69–81.

Mathematical modeling of the glucose–insulin system. is a paper that organizes several models for the glucose-insulin system. 

Excerpts

The glucose–insulin system offers one of the clearest and simplest examples of homeostatic control in the organism.

Essentially a single hormone (insulin) is secreted by the β-cells of the pancreas in response to rising glucose concentrations (hyperglycemia).

A number of hormones contribute to rescuing the organism from hypoglycemia (adrenalin, glucagon, growth hormone, cortisol).

Created diagram 

Nice to have alongside

Fox SI, Human physiology, twelfth edition, McGrawHill, 2011.

Differential Equations and Mathematical Biology (book in light spot)

Jones DS, Sleeman BD, Differential Equations and Mathematical Biology. Chapman&Hall/CRC Mathematical Biology and Medicine Series, 2003. 

Differential Equations and Mathematical Biology is book regarding classical mathematical models using differential equations. It is intended to be educative rather than state of the art.