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Four patients had persistence of disease despite multiple endoscopic excisions.
The following theorem is on the uniform persistence of disease.
Finally, for the convenience of further statements, we introduce the definition on the uniform persistence of disease.
In model (1), the value of the basic reproductive number (mathscr{R}_{0}) determines extinction and persistence of disease.
In this section, we will give a condition for the persistence of disease in epidemic model (2), and our main result is presented by the following theorem.
Figure 3 Time sequence diagram and phase diagram of model ( 4 ) for extinctions of disease 2 and persistence of disease 1.
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Diseases such as pneumonia, metal poisoning, or septicemia (the persistence of disease-causing bacteria in the bloodstream) may cause the mildest type of degeneration parenchymatous changes, or cloudy swelling of the cells; the cells first affected are the specialized cells of the liver and the kidney.
Most research works on discrete epidemic models concern the definition of the basic reproductive number, the global stability of the disease free equilibrium, the persistence of diseases, the existence and local stability of endemic equilibria, the existence of flip bifurcation and Hopf bifurcation.
At the following evaluation both the physician in charge and parents preferred to discontinue canakinumab due to the persistence of disease-associated symptoms (arthralgia and malaise), the presence of possible side effects (dizziness) and the remarkable elevation of acute phase reactants.
Nonetheless, identifying the underlying ecological mechanisms driving the emergence and persistence of diseases is essential to reduce disease risk in human populations (Roche and Guégan, 2011).
In addition to environmental factors and increased life expectancy, intrinsic host responses, such as local and systemic inflammation, immune responses and remodeling [ 17], have key roles in the initiation and persistence of diseases and co-morbidities.
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