Reproduction numbers of infectious disease models

• Main Author: Pauline van den Driessche
• Format: Article
• Language: English
• Published: KeAi Communications Co., Ltd. 2017-08-01
• Series: Infectious Disease Modelling
• Online Access: http://www.sciencedirect.com/science/article/pii/S2468042717300209

This primer article focuses on the basic reproduction number, â0, for infectious diseases, and other reproduction numbers related to â0 that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of â0 determining whether or not the disease dies out. The next generation matrix method of calculating â0 in a compartmental model is described and illustrated. To address control strategies, type and target reproduction numbers are defined, as well as sensitivity and elasticity indices. These theoretical ideas are then applied to models that are formulated for West Nile virus in birds (a vector-borne disease), cholera in humans (a disease with two transmission pathways), anthrax in animals (a disease that can be spread by dead carcasses and spores), and Zika in humans (spread by mosquitoes and sexual contacts). Some parameter values from literature data are used to illustrate the results. Finally, references for other ways to calculate â0 are given. These are useful for more complicated models that, for example, take account of variations in environmental fluctuation or stochasticity. Keywords: Basic reproduction number, Disease control, West Nile virus, Cholera, Anthrax, Zika virus