Stochastic two-group models with transmission dependent on host infectivity or susceptibility

ABSTRACT

Stochastic epidemic models with two groups are formulated and applied to emerging and re-emerging infectious diseases. In recent emerging diseases, disease spread has been attributed to superspreaders, highly infectious individuals that infect a large number of susceptible individuals. In some re-emerging infectious diseases, disease spread is attributed to waning immunity in susceptible hosts. We apply a continuous-time Markov chain (CTMC) model to study disease emergence or re-emergence from different groups, where the transmission rates depend on either the infectious host or the susceptible host. Multitype branching processes approximate the dynamics of the CTMC model near the disease-free equilibrium and are used to estimate the probability of a minor or a major epidemic. It is shown that the probability of a major epidemic is greater if initiated by an individual from the superspreader group or by an individual from the highly susceptible group. The models are applied to Severe Acute Respiratory Syndrome and measles.

KEYWORDS:

• Branching process
• Markov chain
• superspreader

MSC:

• 90D30
• 60J28

Acknowledgments

This research was partially supported by the National Science Foundation [grant number DMS-1517719]. We thank the reviewers and the editor for helpful suggestions on the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Science Foundation, 1517719.