Investigating the impact of vaccine hesitancy on an emerging infectious disease: a mathematical and numerical analysis

ABSTRACT

Throughout the last two centuries, vaccines have been helpful in mitigating numerous epidemic diseases. However, vaccine hesitancy has been identified as a substantial obstacle in healthcare management. We examined the epidemiological dynamics of an emerging infection under vaccination using an SVEIR model with differential morbidity. We mathematically analyzed the model, derived ${\mathcal{R}}_0$, and provided a complete analysis of the bifurcation at ${\mathcal{R}}_0=1$. Sensitivity analysis and numerical simulations were used to quantify the tradeoffs between vaccine efficacy and vaccine hesitancy on reducing the disease burden. Our results indicated that if the percentage of the population hesitant about taking the vaccine is 10%, then a vaccine with 94% efficacy is required to reduce the peak of infections by 40%. If 60% of the population is reluctant about being vaccinated, then even a perfect vaccine will not be able to reduce the peak of infections by 40%.

KEYWORDS:

• Emerging infections
• vaccine hesitancy
• compartmental models & ODEs
• basic reproduction number
• forward bifurcations

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 92-10
• 92-08
• 92B05
• 92D30
• 37G10

Acknowledgments

We would like to thank two anonymous reviewers for feedback that greatly improved our work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Funding from the Simons Foundation (to E.J.S.) is gratefully acknowledged.