- Global stability for an SEIR epidemiological model with varying infectivity and infinite delay
C Connell McCluskey

Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

*Math Biosci Eng* 6:603-10. 2009

..Here, we show that the endemic equilibrium is globally stable for R0 >1. The proof uses a Lyapunov functional that includes an integral over all previous states...

- Attractivity of coherent manifolds in metapopulation models
C Connell McCluskey

Department of Mathematics, Wilfrid Laurier University, 75 University Avenue West, Waterloo, ON N2L3C5, Canada

*J Math Biol* 62:509-41. 2011

..Our methods yield rigorous and practically useful coherence criteria that facilitate useful analyses of ecological and epidemiological problems...

- Global stability for an SEI model of infectious disease with age structure and immigration of infecteds
C Connell McCluskey

Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada Email

*Math Biosci Eng* 13:381-400. 2016

..The model is very appropriate for tuberculosis. A Lyapunov functional is used to show that the unique endemic equilibrium is globally stable for all parameter values. ..

- Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes
C Connell McCluskey

Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

*Math Biosci Eng* 9:819-41. 2012

..For R0 > 1, a Lyapunov functional is used to show that the endemic equilibrium is globally stable amongst solutions for which the disease is present. Finally, some special cases are considered...

- Global stability of an epidemic model with delay and general nonlinear incidence
C Connell McCluskey

Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

*Math Biosci Eng* 7:837-50. 2010

..The global stability proofs use a Lyapunov functional and do not require uniform persistence to be shown a priori. It is shown that the given conditions are satisfied by several common forms of the incidence function...

- Effect of a sharp change of the incidence function on the dynamics of a simple disease
Julien Arino

Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada

*J Biol Dyn* 4:490-505. 2010

..We show that this allows a Hopf bifurcation to occur, with periodic orbits being generated when a locally asymptotically stable equilibrium loses stability...