Effects of behaviour change on HFMD transmission

ABSTRACT

We propose a hand, foot and mouth disease (HFMD) transmission model for children with behaviour change and imperfect quarantine. The symptomatic and quarantined states obey constant behaviour change while others follow variable behaviour change depending on the numbers of new and recent infections. The basic reproduction number ${\mathcal{R}}_0$ of the model is defined and shown to be a threshold for disease persistence and eradication. Namely, the disease-free equilibrium is globally asymptotically stable if ${\mathcal{R}}_0\le 1$ whereas the disease persists and there is a unique endemic equilibrium otherwise. By fitting the model to weekly HFMD data of Shanghai in 2019, the reproduction number is estimated at 2.41. Sensitivity analysis for ${\mathcal{R}}_0$ shows that avoiding contagious contacts and implementing strict quarantine are essential to lower HFMD persistence. Numerical simulations suggest that strong behaviour change not only reduces the peak size and endemic level dramatically but also impairs the role of asymptomatic transmission.

KEYWORDS:

• HFMD
• behaviour change
• basic reproduction number
• infection size
• global stability

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 37N25
• 34D20
• 92D30

Acknowledgments

We thank the two referees for their valuable comments, Dr. Jim Cushing for handling the submission, and Drs. Jifa Jiang and Yijun Lou for helpful suggestions on the draft.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Science Foundation of Shanghai [grant numbers 20ZR1440600 and 20JC1413800], the National Natural Science Foundation of China [grant number 12071300], the Key Research Projects of Beijing Natural Science Foundation-Haidian District Joint Fund [grant number L192012], and the CSU Office of Research through a startup grant.