10176

Kermack-McKendrick Epidemic Model with Time Delay

This Demonstration solves a system of three differential equations with time delays, corresponding to a Kermack–McKendrick epidemic model.

DETAILS

The Kermack–McKendrick model simulates the number of people infected with a contagious illness in a closed population over time. It assumes that the population size is fixed, that the incubation period of the infectious agent is instantaneous, and that the duration of infectivity is the same as the duration of the disease. This model is modified by incorporating a delay time representing the period for incubation, which is the time during which infectious agents develop in the vector; only after that time does the infected vector itself becomes infective, and a delay time for the duration of the infectivity. The model consists of three coupled delay ordinary differential equations and three initial history functions.
,
,
,
.
Here is time, is the number of susceptible people, is the number of infected people, is the number of people who have recovered and developed immunity to the infection, is the infection rate, is the recovery rate, is the incubation period, and is the duration of infectivity. The infection and recovery rates are assumed to be equal to 1. The delay equations are solved using Mathematica's built-in function NDSolve and the results are shown as plots of the number of people in each group versus time and in a three-dimensional parametric plot of the three groups of people. You can change , the period of incubation, and , the duration of infectivity, to follow the trajectory of the solution.

PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.