Hopf bifurcation and global dynamics of time delayed Dengue model

被引：18

作者：

Zafar, Zain Ul Abadin ^{[1
]}

Ali, Nigar ^{[2
]}

Shah, Zahir ^{[3
]}

Zaman, Gul ^{[2
]}

Roy, Prosun ^{[4
]}

Deebani, Wejdan ^{[5
]}

机构：

[1] Univ Cent Punjab, Fac Informat Technol, Lahore, Pakistan

[2] Univ Malakand, Dept Math, Khyber Pakhtunkhwa, Pakistan

[3] King Mongkuts Univ Technol Thonburi, SCL Fixed Point Lab 802, Ctr Excellence Theoret & Computat Sci TaCS CoE, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[4] Univ Wisconsin, Dept Mech Engn, Milwaukee, WI 53201 USA

[5] King Abdulaziz Univ, Coll Arts & Sci, Dept Math, POB 344, Rabigh 21911, Saudi Arabia

来源：

COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE | 2020年 / 195卷

关键词：

Time Delay; Laplace Transform; Hopf Bifurcation; Dengue Internal; Transmission Model; Fractional Differential Equation;

D O I：

10.1016/j.cmpb.2020.105530

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Background and Objective: Dengue viral infections are a standout amongst the supreme critical mosquito borne illnesses nowadays. They create problems like dengue fever (DF), dengue stun disorder (DSS) and dengue hemorrhagic fever (DHF). Lately, the frequency of DHF has expanded considerably. Dengue may be caused by one of serotypes DEN-1 to DEN-4. For the most part, septicity with one serotype presents upcoming defensive resistance against that specific serotype yet not against different serotypes. When anyone is infected for a second time with different serotypes, a serious ailment will occur. The proposed model focused on the dynamic interaction between susceptible cells and free virus cells. The ailment free steady states of the specimen are determined. The steadiness of the steady states has been examined by using Laplace transform. Methods: We introduce an appropriate numerical technique based on an Adams Bash-forth Moulton method for non-integer order delay differential equations. The numerical simulations validate the accuracy and efficacy of the numerical method. Results: In this paper, we study a non-integer order model with temporal delay to elaborate the dynamics of Dengue internal transmission dynamics. The temporal delay is presented in the susceptible cell and free virus cell. Centered on non-integer Laplace transform, some environs on firmness and Hopf bifurcation are derived for the model. Beside these global stability analysis is also done. Lastly, the imitative theoretical results are justified by few numerical simulations. Conclusion: The study spectacles that the non-integer order with temporal-delay can successfully enhance the dynamics and rejuvenate the steadiness terms of non-integer order septicity prototypes. Both the ailment free equilibrium (AFE) node and ailment persistent equilibrium (APE) node are steady for the given system. We deduce a recipe that regulates the critical value at threshold. (c) 2020 Elsevier B.V. All rights reserved.

引用

页数：17

共 31 条

[1] On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems [J].