O’Regan, S.M. & J.M. Drake. 2013. Theory of early warning signals of disease emergence and leading indicators of elimination. Theoretical Ecology 6:333-357. [pdf] [online]

  • This paper presents the basic theory of early warning signals in slow-fast disease transmission systems.

O’Regan, S. M., J.W. Lillie & J.M. Drake. 2016. Leading indicators of mosquito-borne disease elimination. Theoretical Ecology. (In press.) [online]

  • This paper extends the theory of critical slowing down to vector-borne disease systems.

Dibble, C.J., E.B. O’Dea, A.W. Park, & J.M. Drake. 2016. Waiting time to infectious disease emergence. Journal of the Royal Society Interface. (In press.) [online]

  • This paper established the theory of bifurcation delay, derives the probability distribution of the lag that occurs between the time at which an infectious disease becomes critical and the time that outbreak occurs, and shows how these are important to managing emerging and resurgent infectious diseases.

Chen, S. & B. Epureanu. 2016. Regular biennial cycles in epidemics caused by parametric resonance. Journal of Theoretical Biology. (In press.) [online]

  • A novel explanation – parametric resonance – is proposed for the existence of biennial cycles in measles prior to the introduction of vaccines. Stochastic analysis shows that stochasticity can trigger parametric resonance even when the system is in the non-resonance regime of the parameter space.

Bhattacharyya, S. & M.J. Ferrari. 2017. Age-specific mixing generates transient outbreak risk following critical-level vaccination. Epidemiology & Infection 145:12-22. [online]

  • This paper establishes that achieving the theoretical critical vaccination point is insufficient to achieve disease elimination.

Li, S., C. Ma, L. Hao, Q. Su, Z. An, F. Ma, S. Xie, A. Xu, Y. Zhang, Z. Ding, H. Li, L. Cairns, H. Wang, H. Luo, N. Wang, L. Li & M.J. Ferrari. Demographic transition and the dynamics of measles in six provinces in China: A modeling study. PLOS Medicine 14:e1002255. [online]

  • This paper shows that herd immunity and sustained transmission are key determinants of measles dynamics in  China over 30 years.

Drake, J.M. & S.I. Hay. 2017. Monitoring the path to the elimination of infectious diseases. Tropical Medicine & Infectious Disease 2 doi:10.3390/tropicalmed2030020 [online]

  • This paper suggests that critical slowing down can be used to document the approach to disease elimination and shows through simulation that critical slowing down can be robustly detected even in the  presence of significant under-reporting.

Brett, T.S., J.M. Drake & P. Rohani. 2017. Anticipating the emergence of infectious diseases. Journal of the Royal Society Interface 14:20170115.  [online]

  • This paper presents system- and model-independent candidate approaches for anticipating disease emergence prior to large-scale outbreaks using ideas from the theories of dynamical systems and stochastic processes. The paper examines a set of early-warning signals based around the theory of critical slowing down and a likelihood-based approach, and tests the reliability of these two approaches by contrasting theoretical predictions with simulated data.