scholarly journals Low temperatures or high isolation delay increases the average COVID-19 infections in India : A Mathematical modeling approach

2021 ◽  
Vol 9 (1) ◽  
pp. 146-174
Author(s):  
D Bhanu Prakash ◽  
Bishal Chhetri ◽  
D K K Vamsi ◽  
S Balasubramanian ◽  
Carani B Sanjeevi
Keyword(s):  
Low Temperatures ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Equilibrium Points ◽  
Winter Season ◽  
Uniqueness Condition ◽  
High Isolation ◽  
Delay Differential ◽  
The Impact ◽  
Positivity And Boundedness

Abstract The dynamics of COVID-19 in India are captured using a set of delay differential equations by dividing a population into five compartments. The Positivity and Boundedness of the system is shown. The Existence and Uniqueness condition for the solution of system of equations is presented. The equilibrium points are calculated and stability analysis is performed. Sensitivity analysis is performed on the parameters of the model. Bifurcation analysis is performed and the critical delay is calculated. By formulating the spread parameter as a function of temperature, the impact of temperature on the population is studied. We concluded that with the decrease in temperature, the average infections in the population increases. In view of the coming winter season in India, there will be an increase in new infections. This model falls in line with the characteristics that increase in isolation delay increases average infections in the population.

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

scholarly journals Exact and approximate solutions of delay differential equations with nonlocal history conditions

2005 ◽  
Vol 2005 (2) ◽  
pp. 181-194 ◽  
Author(s):  
S. Agarwal ◽  
D. Bahuguna
Keyword(s):  
Differential Equation ◽  
Global Existence ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Approximate Solutions ◽  
Classical Solutions ◽  
Global Existence Of Solutions ◽  
Delay Differential

We study the exact and approximate solutions of a delay differential equation with various types of nonlocal history conditions. We establish the existence and uniqueness of mild, strong, and classical solutions for a class of such problems using the method of semidiscretization in time. We also establish a result concerning the global existence of solutions. Finally, we consider some examples and discuss their exact and approximate solutions.

scholarly journals Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Bahar Ali Khan ◽  
Thabet Abdeljawad ◽  
Kamal Shah ◽  
Gohar Ali ◽  
Hasib Khan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Research Work ◽  
Sufficient Conditions ◽  
Point Of View ◽  
Uniqueness Of The Solution ◽  
Delay Differential ◽  
Ulam Type Stability

AbstractIn this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered. The ensuing problem involves proportional type delay terms and constitutes a subclass of delay differential equations known as pantograph. On using fixed point theorems due to Banach and Schaefer, some sufficient conditions are developed for the existence and uniqueness of the solution to the problem under investigation. Furthermore, due to the significance of stability analysis from a numerical and optimization point of view Ulam type stability and its various forms are studied. Here we mention different forms of stability: Hyers–Ulam (HU), generalized Hyers–Ulam (GHU), Hyers–Ulam Rassias (HUR) and generalized Hyers–Ulam–Rassias (GHUR). After the demonstration of our results, some pertinent examples are given.

scholarly journals The existence and uniqueness theorems of fuzzy delay differential equations

2014 ◽  
Vol 10 (3) ◽  
Author(s):  
Nor Atirah Izzah Zulkefli ◽  
Normah Maan
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Realistic Model ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
New Directions ◽  
Delay Differential ◽  
Real World Problems

Delay differential equations (DDEs) arise many different phenomena including in physics, biology and chemistry. In many cases of the modeling of real world problems, information about the behaviour of a dynamical system is uncertain. In order to obtain a more realistic model, we have to take into account these uncertainties. Therefore, in this paper, we propose the existence and uniqueness theorems for fuzzy time-delay dynamical systems. We finally present some conclusions and new directions for further research in this area.

scholarly journals Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Nasser Hassan Sweilam ◽  
Seham Mahyoub Al-Mekhlafi ◽  
Taghreed Abdul Rahman Assiri
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Numerical Study ◽  
Equilibrium Points ◽  
Fractional Delay ◽  
The Stability ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

A novel mathematical fractional model of multistrain tuberculosis with time delay memory is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the sense of the Grünwald–Letinkov definition. Modified parameters are introduced to account for the fractional order. The stability of the equilibrium points is investigated for any time delay. Nonstandard finite deference method is proposed to solve the resulting system of fractional-order delay differential equations. Numerical simulations show that nonstandard finite difference method can be applied to solve such fractional delay differential equations simply and effectively.

scholarly journals Bifurcation Analysis of a Duopoly Game with R&D Spillover, Price Competition and Time Delays

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 257 ◽  
Author(s):  
B. A. Pansera ◽  
L. Guerrini ◽  
M. Ferrara ◽  
T. Ciano
Keyword(s):  
Continuous Time ◽  
Delay Differential Equations ◽  
Price Competition ◽  
Time Delays ◽  
Equilibrium Points ◽  
Hopf Bifurcations ◽  
Stage Game ◽  
Set Up ◽  
The Stability ◽  
Delay Differential

The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. It is found that the model exhibits very complex dynamical behaviours, and its Nash equilibrium is destabilised via Hopf bifurcations.

scholarly journals Stepanov-Like Asymptotical Almost Periodic Functions and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Yongkun Li ◽  
Yaolu Wang ◽  
Jianglian Xiang
Keyword(s):  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic Functions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Delay Differential

In this paper, we first study some basic properties of Stepanov-like asymptotical almost periodic functions including the completeness of the space of Stepanov-like asymptotical almost periodic functions. Then, as an application, based on these and the contraction mapping principle, we obtain sufficient conditions for the existence and uniqueness of Stepanov-like asymptotical almost periodic solutions for a class of semilinear delay differential equations.

QUALITATIVE BEHAVIOR AND STABILITY OF SOLUTIONS OF A HYBRID SYSTEM

2005 ◽  
Vol 03 (01) ◽  
pp. 17-25 ◽  
Author(s):  
GEORGE SEIFERT
Keyword(s):  
Delay Differential Equations ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Qualitative Behavior ◽  
Dimensional System ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
General Systems ◽  
Two Dimensional System ◽  
Delay Differential

In this paper we consider a certain two-dimensional system of delay differential equations with piecewise constant arguments. We find conditions under which this system has constant solutions; i.e. equilibrium points, and their behavior and stability properties. We also find conditions under which certain of these solutions have a type of chaotic behavior. This paper contains results for more general systems than were dealt with in a previous paper [9].

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