Demographic population cycles and ℛ0 in discretetime epidemic models
| dc.contributor.author | van den Driessche, P. | |
| dc.contributor.author | Yakubu, Abdul-Aziz | |
| dc.date.accessioned | 2021-02-13T07:46:33Z | |
| dc.date.available | 2021-02-13T07:46:33Z | |
| dc.date.copyright | 2018 | en_US |
| dc.date.issued | 2018 | |
| dc.description.abstract | We use a general autonomous discrete-time infectious disease model to extend the next generation matrix approach for calculating the basic reproduction number, R0, to account for populations with locally asymptotically stable period k cycles in the disease-free systems, where k≥1. When R0<1 and the demographic equation (in the absence of the disease) has a locally asymptotically stable period k population cycle, we prove the local asymptotic stability of the disease-free period k cycle. That is, the disease goes extinct whenever R0<1. Under the same period k demographic assumption but with R0>1, we prove that the disease-free period k population cycle is unstable and the disease persists. Using the Ricker recruitment function, we apply our results to discrete-time infectious disease models that are formulated for Susceptible-Infectious-Recovered (SIR) infections with and without vaccination, and Infectious Salmon Anemia Virus (ISAv) infections in a salmon population. When R0>1, our simulations show that the disease-free period k cycle dynamics drives the SIR disease dynamics, but not the ISAv disease dynamics. | en_US |
| dc.description.reviewstatus | Reviewed | en_US |
| dc.description.scholarlevel | Faculty | en_US |
| dc.description.sponsorship | This research was partially supported by NSERC, through a Discovery Grant (P.vdD.). A.-A.Y. was partially supported by DHS Center Of Excellence for Command, Control and Interoperability at Rutgers University, NSF Computational Sustainability Grant # CCF - 1522054, and NSF Award # DMS-1743144. | en_US |
| dc.identifier.citation | van den Driessche, P. & Yakubu, A. (2018). Demographic population cycles and ℛ0 in discrete-time epidemic models. Journal of Biological Dynamics, 13(1), 179-200. https://doi.org/10.1080/17513758.2018.1537449 | en_US |
| dc.identifier.uri | https://doi.org/10.1080/17513758.2018.1537449 | |
| dc.identifier.uri | http://hdl.handle.net/1828/12677 | |
| dc.language.iso | en | en_US |
| dc.publisher | Journal of Biological Dynamics | en_US |
| dc.subject.department | Department of Mathematics and Statistics | |
| dc.title | Demographic population cycles and ℛ0 in discretetime epidemic models | en_US |
| dc.type | Article | en_US |