A verbal model of predator-prey cycles: 1.Predators eat prey and reduce their numbers 2.Predators go hungry and decline in number 3.With fewer predators, prey survive better and increase 4.Increasing prey populations allow predators to increase...........................And repeat… 4
Why don’t predators increase at the same time as the prey? 5
7 The Lotka-Volterra Model: Assumptions 1.Prey grow exponentially in the absence of predators. 2.Predation is directly proportional to the product of prey and predator abundances (random encounters). 3.Predator populations grow based on the number of prey. Death rates are independent of prey abundance.
Generic Model f(x) prey growth term g(y) predator mortality term h(x,y) predation term e prey into predator biomass conversion coefficient
Neurons generate and propagate electrical signals, called action potentials Neurons pass information at synapses: The presynaptic neuron sends the message. The postsynaptic neuron receives the message. Human brain contains an estimated 10 11 neurons – Most receive information from a thousand or more synapses – There may be as many as 10 14 synapses in the human brain.
Neuronal Communication Transmission along a neuron
Action Potential How the neuron ‘sends’ a signal
Lifespan of an HIV Infection Points to Note: Time in Years T-Cell count relatively constant over a week
HIV Infection Model (Perelson- Kinchner) Modeling T-Cell Production: – Assumptions: Some T-Cells are produced by the lymphatic system Over short time the production rate is constant At longer times the rate adjusts to maintain a constant concentration T-Cells are produced by clonal selection if an antigen is present but the total number is bounded T-Cells die after a certain time
Model I We guess that behavior is captured by the drift and the diffusivity is the bulk diffusivity Use the following model Simulate using Monte Carlo methods Calculate the ‘bio-diffusivity’ and compare with MD results