One of the simplest mathematical models for transmission of an infectious disease is the so-called SIR (Susceptible/Infected/Recovered) model. After explaining the setup of the model, we explore what it tells us about the spread of an infection such as COVID-19.
One of the simplest mathematical models for transmission of an infectious disease is the so-called SIR (Susceptible/Infected/Recovered) model. After explaining the setup of the model, we explore what it tells us about the spread of an infection such as COVID-19. The reproduction number (R) quantifies the average number of infections caused by an infected individual. If R is greater than one, the infection can spread. R depends on features such as the duration of infection, the number of contacts people make, the probability of transmission when an infected person meets a susceptible person, and the fraction of the population that is susceptible. Thinking about R lets us figure out how effective control measures need to be in order to dampen transmission. It also explains herd immunity: infection can no longer increase if there are not enough susceptible people in the population to maintain transmission. Finally, we explore the consequences of prematurely relaxing control measures.
With training in both mathematics and biology, Alun L. Lloyd, Ph.D. is a mathematical biologist who primarily works on modeling the spread of infectious diseases. He was born and raised in Wales. As an undergraduate, he studied mathematics at Trinity College, Cambridge University, before moving to the University of Oxford to do a doctorate in Zoology. He came to the US in 1999, first at the Institute of Advanced Study (Princeton, NJ)--a place whose most famous faculty member was Albert Einstein. Since 2003 he has been at NC State, where he is now Drexel Professor of Mathematics and Director of the Biomathematics Graduate Program. Dr. Lloyd’s work takes him to many beautiful locations around the world, including Australia, South Africa, Peru, and many places in Europe and the US. When he am not thinking about math or biology, he loves to hike, particularly in the mountains and the desert of Utah and Arizona.