Can infectious diseases eradicate host species? The effect of infection-age structure

• Published in: Mathematical biosciences and engineering : MBE Vol. 20; no. 10; pp. 18717 - 18760
• Main Authors: Ponce, Joan, Thieme, Horst R.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-01-2023
• Subjects: a priori estimates; host extinction; host persistence; incidence function; integral equations; kermack; laplace transform; mckendrick; uniform weak persistence; volterra functional equations
• ISSN: 1551-0018; 1551-0018
• DOI: 10.3934/mbe.2023830

It is a fundamental question in mathematical epidemiology whether deadly infectious diseases only lead to a mere decline of their host populations or whether they can cause their complete disappearance. Upper density-dependent incidences do not lead to host extinction in simple, deterministic SI or SIS (susceptible-infectious) epidemic models. Infection-age structure is introduced into SIS models because of the biological accuracy offered by considering arbitrarily distributed infectious periods. In an SIS model with infection-age structure, survival of the susceptible host population is established for incidences that depend on the infection-age density in a general way. This confirms previous host persistence results without infection-age for incidence functions that are not generalizations of frequency-dependent transmission. For certain power incidences, hosts persist if some infected individuals leave the infected class and become susceptible again and the return rate dominates the infection-age dependent infectivity in a sufficient way. The hosts may be driven into extinction by the infectious disease if there is no return into the susceptible class at all.