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The effect of incidence functions on the dynamics of a quarantine/isolation model with time delay. (English) Zbl 1208.34127
Summary: The problem of the asymptotic dynamics of a quarantine/isolation model with time delay, subject to two incidence functions, namely standard incidence and the Holling type II (saturated) incidence function, is considered. Rigorous qualitative analysis of the model shows that it exhibits essentially the same (equilibrium) dynamics regardless of which of the two incidence functions is used. In particular, for each of the two incidence functions, the model has a globally asymptotically stable disease-free equilibrium whenever the associated reproduction threshold quantity is less than unity. Further, it has a unique endemic equilibrium when the threshold quantity exceeds unity. For the case with the Holling type II incidence function, it is shown that the unique endemic equilibrium of the model is globally asymptotically stable for a special case. The permanence of the disease is also established for the model with the Holling type II incidence function. Finally, numerical simulations of the model with standard incidence show that the disease burden decreases with increasing time delay (incubation period).

MSC:
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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