A discrete‐time anthrax model in human and herbivore populations. (31st October 2018)

• Record Type: Journal Article
• Authors: Yakubu, Abdul‐Aziz; Ziyadi, Najat
• Other Names: Leander Rachel guestEditor.; Ding Wandi guestEditor.; Salinas René A. guestEditor.
• Is Part Of: Natural resource modelling. Volume 31:Number 4(2018:Nov.)
• Page Start: N/A
• Page End: N/A
• Publication Date: 2018-10-31
• Subjects: anthrax -- discrete‐time model -- herbivore and human populations; Conservation of natural resources -- Mathematical models -- Periodicals; Ecology -- Mathematical models -- Periodicals; 371.397
• DOI: 10.1111/nrm.12192
• Languages: English
• ISSNs: 0890-8575

Abstract

Abstract: We introduce a discrete‐time anthrax disease model in human and herbivore populations, where the herbivore recruitment function is the classic Beverton–Holt model while that of humans is a constant recruitment function. We use the next generation method to compute the basic reproduction numbers for the submodels consisting of only herbivores ( R 0 A ) and only humans ( R 0 H ) . In addition, we compute it for the full human–herbivore model ( R 0 A H ) . When R 0 A < 1 or R 0 H < 1 or R 0 A H < 1, the number of anthrax infections decreases and the disease does not invade the corresponding population. Whereas, the number of anthrax infections increases and the disease invades the corresponding population when R 0 A > 1 or R 0 H > 1 or R 0 A H > 1 . Our simulations show that it is possible for the anthrax disease to invade a human–herbivore population where the disease does not invade either herbivores or humans in isolation. Recommendations for resource managers To help guide anthrax disease prevention and control strategies, we provide basic reproduction numbers for the herbivore only population ( R 0 A ), human‐only population ( R 0 A ) and human–herbivore population ( R 0 A H ) . R 0 < 1 implies the number of anthrax infections deceases and anthrax does not invade the population, while R 0 > 1 implies the number of anthrax cases increases and anthrax invasion occurs. It is possible for anthrax to invade a population consisting of herbivores and humans where the disease does not invade either the herbivores or humans in isolation. Thus, more anthrax surveillance is required in mixed populations of herbivores and humans. Our human–herbivore model can be used to predict the number of anthrax‐infected humans and animals given the number of known anthrax infections in populations.