Biological Models in Python

human-computer interaction

bridge between human intention and machine action, instruct computers to carry out desired tasks

abstraction

turns the complex operations of a computer into more understable form for humans (instead of binary, programmers use a language that is close to a human language but precise enough for a computer to understand)

syntax

refers to structure or form of the code

semantics

refers to meaning behind the code

sequential

an algorithm consists of well-defined steps that goes in order

input

data that the algorithm process

output

result after processing the input

deterministic

given the same input, it will always produce the same output

interpreted language

python is a compiled language or an interpreted language

interpreted language

code is executed line by line from an interactable UI

ease, readability, interpreted language, versatility, libraries

why python?

abstract and simplify complex systems, quantify biological phenomena, predict outcomes and test hypotheses, explore unobservable phenomena

benefits of using biological models

epidemiology

understand how infectious diseases spread and how they can be controlled

population dynamics

how populations of organisms change over time

neuroscience

how the brain processes information, how neurons communicate, how networks of neurons give rise to behavior and cognition

dynamical system

describes any system that changes or evolves over time according to a specific set of rules

state of the system and evolution over time

key properties of a dynamical system

state of the system

set of variable that describe the system at a given point in time

deterministic system

the future state of the system is entirely determined by its current state and the rules governing it. no randomness

stochastic system

some randomness, future state in not entirely predictable

continuous system

state variables change smoothly over time and evolution of the system is described by differential equations

discrete systems

the state variables change at specific intervals of time and the evolution of the system is described by difference quations

break

how to leave a while loop

continue

how to stop processing current iteration of loop and immediately go to the next one

assert

will check to make sure that something is true during the course of a program

range()

returns a list of numbers from 0 up to but not including the number we pass it

filter

determines whether expression is performed on each member of the list

immutable

tuple is mutable or immutable

immutable

strings are mutable or immutable

mutable

lists are mutable or immutable

mutable

a variable whose value can change multiple times

immutable

a variable whose value cannot be changes once its assigned

faster

benefit of immutability of tuples

append

takes a singleton as an argument

extend

takes a list as an argument

list

slower but more powerful than tuples

dictionaries

store values, ordered, changeable, do not allow duplicates

none

equivalent to false and the special value returned bu functions with no return

john snow

father of epidemiology

susceptible, infected, recovered

3 states in SIR model

no births or deaths, population is homogeneously mixes

sir model assumes

N

S+I+R=

R0

represents the expected number of people an initially infected person will infect (SIR)

R0

basic reproductive number

alpha

chance of transmission in SIR

gamma

average duration of an illness SIR

lotka-volterra

predator-prey equations that describe the dynamics of biological systems in which two species interact, captures the oscillatory nature of predator-prey populations over time

r

natural growth rate of prey in absence of predators(LV)

alpha

predation rate coefficient(rate at which predators destroy prey) LV

N

number of prey (LV)

beta

efficiency of turning consumed prey into predators (LV)

d

natural death rate of predators in absence of prey (LV)

P

number of predators(LV)

numpy

fundamental library for scientific computing in python that provides support for arrays and matrices

numpy array

more compact and faster than python lists due to optimized C code under the hood

hooke’s law model

a particle of mass m attached to the end of an ideal spring with equilibrium length zero

restoring force

the spring exerts a force proportional to the displacement and opposite direction

k

spring constant

euler’s method

approximates the solution of differential equations by stepping forward in small increments using the derivative at the current point

molecular dynamics

set of algorithms designed to describe the evolution of a system of particles interacting via a given force field following newtonian dynamics