QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.

An Asymptotic-Fitted Method for Solving Singularly Perturbed Delay Differential Equations

In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the new equation, we introduced a fitting parameter and determined its value using the theory of singular Perturbation;O’Malley [1]. The three term recurrence relation obtained is solved using Thomas algorithm. The applicability of the method is tested by considering five linear problems (two problems on left layer and one problem on right layer) and two nonlinear problems.

Modelling COVID-19 epidemic with confirmed cases-driven contact tracing quarantine

The pandemic of novel coronavirus disease 2019(COVID-19)has been a severe threat to public health.The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak.In this paper,we developed a mathematical model of the COVID-19 epidemic with confirmed case-driven contact tracing quarantine,and applied the model to evaluate the effectiveness of the policy of contact tracing and quarantine.The model is established based on the combination of the compartmental model and individual-based model simulations,which results in a closed-form delay differential equation model.The proposed model includes a novel form of quarantine functions to represent the number of quarantine individuals following the confirmed cases every day and provides analytic expressions to study the effects of changing the quarantine rate.The proposed model can be applied to epidemic dynamics during the period of community spread and when the policy of confirmed cases-driven contact tracing quarantine is efficient.We applied the model to study the effectiveness of contact tracing and quarantine.The proposed delay differential equation model can describe the average epidemic dynamics of the stochastic-individual-based model,however,it is not enough to describe the diverse response due to the stochastic effect.Based on model simulations,we found that the policy of contact tracing and quarantine can obviously reduce the epidemic size,however,may not be enough to achieve zero-infectious in a short time,a combination of close contact quarantine and social contact restriction is required to achieve zeroinfectious.Moreover,the effect of reducing epidemic size is insensitive to the period of quarantine,there are no significant changes in the epidemic dynamics when the quarantine days vary from 7 to 21 days.

A Spectrum Relation of Almost Periodic Solution of Second Order Scalar Functional Differential Equations with Piecewise Constant Argument

In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.