Biologists use and create mathematical models in order to

Last updated: 5/22/2023

Biologists use and create mathematical models in order to predict outcomes of various systems they are studying For example A population biologist studying a specific population will want to predict how fast the population is growing and what is the maximum population that can be reached An epidemiologist studying a disease virus needs to make predictions as to how fast the virus is spreading and what the total number of infected might be One model that is used in both those scenarios is the so called Logistics function In this project we will show how to use this function to help model the spread of a virus The logistics equation is given as the solution to the following differential equation T N t rN t No dt where r is the growth rate N t is the total number of people infected at time t No is the maximum number of people that will be infected The solution to this differential equation is called the Logistics Function and is given by the formula Noo N t N t 1 e rt No where No is the initial number of people infected and t is time measured in days past the initial starting time To prepare medical institutions to function in an optimal way during an epidemic it is important to know the number of infected people per day This is so we can find the maximum number of people that will be infected per day so the institutions can expect when the peak infections will be The time T that corresponds to the maximum number of people infected per day is called the epidemic peak We can find the infected number of people per day by differentiating the Logistics function N t from this we can then determine the epidemic peak time T N 2