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Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites

T. DhirasakdanonH. R. Thieme — 2010

Mathematical Modelling of Natural Phenomena

For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...

Semilinear perturbations of Hille-Yosida operators

Horst R. ThiemeHauke Vosseler — 2003

Banach Center Publications

The semilinear Cauchy problem (1) u’(t) = Au(t) + G(u(t)), u ( 0 ) = x D ( A ) ¯ , with a Hille-Yosida operator A and a nonlinear operator G: D(A) → X is considered under the assumption that ||G(x) - G(y)|| ≤ ||B(x -y )|| ∀x,y ∈ D(A) with some linear B: D(A) → X, B ( λ - A ) - 1 x = λ 0 e - λ t V ( s ) x d s , where V is of suitable small strong variation on some interval [0,ε). We will prove the existence of a semiflow on [ 0 , ) × D ( A ) ¯ that provides Friedrichs solutions in L₁ for (1). If X is a Banach lattice, we replace the condition above by |G(x) - G(y)| ≤ Bv whenever...

An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective

H. R. ThiemeA. TridaneY. Kuang — 2008

Mathematical Modelling of Natural Phenomena

A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those that had contact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the first place. The model considers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that treated uninfected...

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