Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection

Julien Arino; Evan Milliken

doi:10.1007/s00285-022-01765-9

Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection

J Math Biol. 2022 Jun 23;84(7):61. doi: 10.1007/s00285-022-01765-9.

Authors

Julien Arino¹, Evan Milliken²

Affiliations

¹ Department of Mathematics & Data Science Nexus, University of Manitoba, Winnipeg, Manitoba, Canada.
² Department of Mathematics, University of Louisville, Louisville, Kentucky, United States. Evan.Milliken@louisville.edu.

Abstract

Various vaccines have been approved for use to combat COVID-19 that offer imperfect immunity and could furthermore wane over time. We analyze the effect of vaccination in an SLIARS model with demography by adding a compartment for vaccinated individuals and considering disease-induced death, imperfect and waning vaccination protection as well as waning infections-acquired immunity. When analyzed as systems of ordinary differential equations, the model is proven to admit a backward bifurcation. A continuous time Markov chain (CTMC) version of the model is simulated numerically and compared to the results of branching process approximations. While the CTMC model detects the presence of the backward bifurcation, the branching process approximation does not. The special case of an SVIRS model is shown to have the same properties.

Keywords: Backward bifurcation; Branching process approximation; Continuous time Markov chain; Epidemic model; Waning immunity.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

COVID-19* / epidemiology
COVID-19* / prevention & control
Humans
Markov Chains
Models, Biological
Vaccination
Vaccines*

Substances

Vaccines