Incorporating mass vaccination into compartment models for infectious diseases

Glenn Ledder; Glenn Ledder

doi:10.3934/mbe.2022440

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 9457-9480. doi: 10.3934/mbe.2022440

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Incorporating mass vaccination into compartment models for infectious diseases

Glenn Ledder ^,

Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA

Received: 26 April 2022 Revised: 08 June 2022 Accepted: 14 June 2022 Published: 29 June 2022

The standard way of incorporating mass vaccination into a compartment model for an infectious disease is as a spontaneous transition process that applies to the entire susceptible class. The large degree of COVID-19 vaccine refusal, hesitancy, and ineligibility, and initial limitations of supply and distribution require reconsideration of this standard treatment. In this paper, we address these issues for models on endemic and epidemic time scales. On an endemic time scale, we partition the susceptible class into prevaccinated and unprotected subclasses and show that vaccine refusal/hesitancy/ineligibility has a significant impact on endemic behavior, particularly for diseases where immunity is short-lived. On an epidemic time scale, we develop a supply-limited Holling type 3 vaccination model and show that it is an excellent fit to vaccination data. We then extend the Holling model to a COVID-19 scenario in which the population is divided into two risk classes, with the high-risk class being prioritized for vaccination. In both cases, with and without risk stratification, we see significant differences in epidemiological outcomes between the Holling vaccination model and naive models. Finally, we use the new model to explore implications for public health policies in future pandemics.
- vaccination,
- COVID-19,
- compartment models,
- epidemic disease models,
- endemic disease models
Citation: Glenn Ledder. Incorporating mass vaccination into compartment models for infectious diseases[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9457-9480. doi: 10.3934/mbe.2022440

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Abstract

The standard way of incorporating mass vaccination into a compartment model for an infectious disease is as a spontaneous transition process that applies to the entire susceptible class. The large degree of COVID-19 vaccine refusal, hesitancy, and ineligibility, and initial limitations of supply and distribution require reconsideration of this standard treatment. In this paper, we address these issues for models on endemic and epidemic time scales. On an endemic time scale, we partition the susceptible class into prevaccinated and unprotected subclasses and show that vaccine refusal/hesitancy/ineligibility has a significant impact on endemic behavior, particularly for diseases where immunity is short-lived. On an epidemic time scale, we develop a supply-limited Holling type 3 vaccination model and show that it is an excellent fit to vaccination data. We then extend the Holling model to a COVID-19 scenario in which the population is divided into two risk classes, with the high-risk class being prioritized for vaccination. In both cases, with and without risk stratification, we see significant differences in epidemiological outcomes between the Holling vaccination model and naive models. Finally, we use the new model to explore implications for public health policies in future pandemics.

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