Dynamics of SI epidemic with a demographic Allee effect

• Published in: Theoretical population biology 2015-12, Vol.106, p.1-13
• Main Authors: Usaini, Salisu, Anguelov, Roumen, Garba, Salisu M.
• Format: Article
• Language: English
• Subjects: Algorithms; Allee effect; Animals; Carrying capacity; Communicable Diseases - mortality; Communicable Diseases - transmission; Demography; Epidemics; Extinction; Extinction, Biological; Humans; Models, Biological; Persistence; Population Density; Population Dynamics; Threshold
• ISSN: 0040-5809; 1096-0325
• DOI: 10.1016/j.tpb.2015.10.005

In this paper, we present an extended SI model of Hilker et al. (2009). In the presented model the birth rate and the death rate are both modeled as quadratic polynomials. This approach provides ample opportunity for taking into account the major contributors to an Allee effect and effectively captures species’ differential susceptibility to the Allee effects. It is shown that, the behaviors (persistence or extinction) of the model solutions are characterized by the two essential threshold parameters λ0 and λ1 of the transmissibility λ and a threshold quantity μ∗ of the disease pathogenicity μ. If λλ0 and μλ1 and μ>μ∗, the disease derives the host population to extinction with origin as the only global attractor. For the special cases of the model, verifiable conditions for host population persistence (with or without infected individuals) and host extinction are derived. Interestingly, we show that if the values of the parameters α and β of the extended model are restricted, then the two models are similar. Numerical simulations show how the parameter β affects the dynamics of the model with respect to the host population persistence and extinction. •We extend an SI model of Hilker et al. (2009) by modeling demographics as quadratic polynomials.•Allee effect in host demographics might play a stabilizing and preventive role in the invasion of disease.•An additional disease-related death increases the likelihood of population extinction.•Verifiable conditions that guarantee host persistence and extinction are derived.•There is an effective increase in the Allee threshold when a disease invades a population.