Asymptotic convergence in delay differential equations arising in epidemiology and physiology. (English) Zbl 1483.34115
This paper investigates the dynamics of a general broad class of delay differential equation, especially for the presence of oscillations. On the other hand, this paper devotes to proving that the global attraction towards a nontrivial equilibrium could be reduced to the nonexistence of solutions of a certain system of inequalities. Their theoretical results are easily applicable and cover situations in which the global attraction critically depends on the delay compared with the precious works.
For the application of the theoretical results, this paper emphasizes two examples, that is, epidemic models with awareness and the production of platelets. In epidemiology, the different types of population awareness and the time delays of individuals’ responses to available information about the disease play a critical role in its spread. Using the theoretical results, they describe qualitative properties of the behavioral responses that prevent the presence of sustainable oscillations in the number of infected individuals. On the other hand, for physiological models, they discuss the influence of some biological parameters in certain anomalies in the production of platelets.
Above all, the idea of this work is novel with the theoretical analysis and application. Meanwhile, this paper focus on the dynamics of a general broad class of delay differential equation, whose results have generality. Consequently, this paper can be regarded as a significant work in mathematical biology.
For the application of the theoretical results, this paper emphasizes two examples, that is, epidemic models with awareness and the production of platelets. In epidemiology, the different types of population awareness and the time delays of individuals’ responses to available information about the disease play a critical role in its spread. Using the theoretical results, they describe qualitative properties of the behavioral responses that prevent the presence of sustainable oscillations in the number of infected individuals. On the other hand, for physiological models, they discuss the influence of some biological parameters in certain anomalies in the production of platelets.
Above all, the idea of this work is novel with the theoretical analysis and application. Meanwhile, this paper focus on the dynamics of a general broad class of delay differential equation, whose results have generality. Consequently, this paper can be regarded as a significant work in mathematical biology.
Reviewer: Xiao Wang (Changsha)
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 92D30 | Epidemiology |
| 34K25 | Asymptotic theory of functional-differential equations |
| 34K11 | Oscillation theory of functional-differential equations |
Keywords:
delay-dependent criteria; attraction; nonmonotone equations; SIS model with awareness; platelet productionReferences:
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