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Biomathematics
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- 2. What is Biomathematics? It is the use of mathematical models to help understand phenomena in biology. Term was coined by William Moses feldman. It has been used in areas such as cellular neurobiology, epidemic modeling and population genetics.
- 3. Population Problems • Predator-Prey •X= Hare population • Y= Lynx population dx/dt= ax– bxy, dy/dt= –cy+pxy,
- 4. Spread of Disease Hongkong flu Corona virus graph Pre-vaccine flu related pneumonia
- 5. SIR Model Susceptibles S InfectedI Recovered R
- 6. “ ” Patterns in Nature • Chemicalsthat react and diffuse in animal coats make visible pattern • c(x,t) concentration at time t location x.
- 7. “ ” Embryo Development-genes • Youngembryos form a body axis early • Why? How? Chemicals cause cells to move
- 8. Models Reproduce experiments • n=cell density • u= chemical
- 9. Species interaction • Waggle dance performedby honey bee was decoded using Markov model of bee foraging behavior by various mathematicians.
- 10. Visual System • Theelectrical firing rate of your visual system neurons changes with stimulus angle!
- 11. Each neuron canbe modeled. Ions move across membrane Voltage V changes in time.
- 12. Ischmic Wound The woundswhich occur due to reduced blood flow. Mathematical models of angiogenic networks Were developed by Mcdougall and coworkers in connection with chemotherapeutic strategies
- 13. Enzyme kinetics Enzyme kineticsis the study of chemical reactions that are catalyzed by enzyme. It provides information about the diverse range of reactions in the human body. Michaelis Menton equation
- 14. Conclusion • There willbe more math in biology and medicine in your lifetime. • Unlike other science the math models are being discovered right now
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