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Models arising in biology are often written in terms of Ordinary Differential Equations. The celebrated paper of Kermack-McKendrick (19271, founding mathematical epidemiology, showed the necessity to include parameters in order to describe the state of the individuals, as time elapsed after infection. During the 70s, many mathematical studies were developed when equations are structured by age, size, more generally a physiological trait. The renewal, growth-fragmentation are the more standard equations. The talk will present structured equations, show that a universal generalized relative entropy structure is available in the linear case, which imposes relaxation to a steady state under non-degeneracy conditions. In the nonlinear cases, it might be that periodic solutions occur, which can be interpreted in biological terms, e.g., as network activity in the neuroscience. When the equations are conservation laws, a variant of the Monge-Kantorovich distance (called Fortet-Mourier distance) also gives a general non-expansion property of solutions.
Event date: 19/1/2023
Speaker: Prof. Benoît Perthame (Sorbonne University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Biology and Mathematics and Statistics
- Keywords:
- Biomathematics Equations
- Resource Type:
- Video
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Video
What if we looked at Parkinson's as an neurological electrical problem? Brain researcher Eleftheria Pissadaki and her team study dopamine neurons, the neurons that selectively die during Parkinson's. They discovered that the bigger a neuron is, the more vulnerable it becomes because it simply requires more energy. This new insight is reframing the disease -- and by "finding the fuse box for each neuron" and figuring out how much energy it needs, may help us neuroprotect our brain cells.
- Subjects:
- Health Sciences and Mathematics and Statistics
- Keywords:
- Brain -- Diseases -- Research Brain -- Mathematical models
- Resource Type:
- Video