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- Andrei Korobeinikov
- Bulletin of mathematical biology
- 2004

Lyapunov functions for basic virus dynamics models are introduced, and global stability of the models are thereby established.

- Andrei Korobeinikov
- Bulletin of mathematical biology
- 2006

Lyapunov functions for two-dimension SIR and SIRS compartmental epidemic models with non-linear transmission rate of a very general form f(S, I) constrained by a few biologically feasible conditionsâ€¦ (More)

- Andrei Korobeinikov
- Bulletin of mathematical biology
- 2007

We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission isâ€¦ (More)

- Andrei Korobeinikov
- Mathematical medicine and biology : a journal ofâ€¦
- 2004

Lyapunov functions for classic SEIR and SEIS compartmental epidemic models, including those with vertical and horizontal transmission, are introduced. Global properties of the models is therebyâ€¦ (More)

- Andrei Korobeinikov, Philip K. Maini
- Mathematical medicine and biology : a journal ofâ€¦
- 2005

In this paper we consider the impact of the form of the non-linearity of the infectious disease incidence rate on the dynamics of epidemiological models. We consider a very general form of theâ€¦ (More)

- Andrei Korobeinikov, Philip K. Maini
- Mathematical biosciences and engineering : MBE
- 2004

Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form betaI(p)S(q) for the case p </= 1 are constructed. Global stability of the models isâ€¦ (More)

- Andrei Korobeinikov, Graeme C. Wake
- Appl. Math. Lett.
- 2002

Lyapunov functions for classical SIR, SIRS, and SIS epidemiological models 8re introduced. Global stability of the endemic equilibrium states of the models is thereby established. @ 2002 Elsevierâ€¦ (More)

- Andrei Korobeinikov
- Mathematical medicine and biology : a journal ofâ€¦
- 2009

Establishing the conditions for the stability of ecosystems and for stable coexistence of interacting populations is a problem of the highest priority in mathematical biology. This problem is usuallyâ€¦ (More)

- Vincent Calvez, Andrei Korobeinikov, Philip K. Maini
- Journal of theoretical biology
- 2005

Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim ofâ€¦ (More)

- Andrei Korobeinikov
- Bulletin of mathematical biology
- 2009

We consider global properties of compartment SIR and SEIR models of infectious diseases, where there are several parallel infective stages. For instance, such a situation may arise if a fraction ofâ€¦ (More)