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Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18717-18760. doi: 10.3934/mbe.2023830
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Can infectious diseases eradicate host species? The effect of infection-age structure

  • School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, USA
  • Dedicated to Stephan Luckhaus on the occasion of his 70th birthday.
  • Received: 29 July 2023 Revised: 18 September 2023 Accepted: 21 September 2023 Published: 09 October 2023

  • 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.

    Citation: Joan Ponce, Horst R. Thieme. Can infectious diseases eradicate host species? The effect of infection-age structure[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18717-18760. doi: 10.3934/mbe.2023830

    Related Papers:

  • 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.


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