scholarly journals Mathematical analysis of a fractional-order epidemic model with nonlinear incidence function

2021 ◽  
Vol 7 (2) ◽  
pp. 2160-2175
Author(s):  
Salih Djillali ◽  
◽  
Abdon Atangana ◽  
Anwar Zeb ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Fractional Order ◽  
Graphical Representation ◽  
Order Model ◽  
Derivative Operator ◽  
Nonlinear Incidence ◽  
Incidence Function ◽  
Different Types ◽  
Fractional System ◽  
Nonlinear Incidence Function

<abstract><p>In this paper, we are interested in studying the spread of infectious disease using a fractional-order model with Caputo's fractional derivative operator. The considered model includes an infectious disease that includes two types of infected class, the first shows the presence of symptoms (symptomatic infected persons), and the second class does not show any symptoms (asymptomatic infected persons). Further, we considered a nonlinear incidence function, where it is obtained that the investigated fractional system shows some important results. In fact, different types of bifurcation are obtained, as saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation, where it is discussed in detail through the research. For the numerical part, a proper numerical scheme is used for the graphical representation of the solutions. The mathematical findings are checked numerically.</p></abstract>

Comparison of two different types of fractional-order COVID-19 distributed time-delay models with real data application

2021 ◽  
pp. 2150219
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xinjian Zhuo
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Distributed Delay ◽  
Real Data ◽  
Least Square ◽  
Order Model ◽  
The Real ◽  
Fractional Order Model ◽  
Different Types ◽  
Distributed Time Delay

The outbreak of COVID-19 has a great impact on the world. Considering that there are different infection delays among different populations, which can be expressed as distributed delay, and the distributed time-delay is rarely used in fractional-order model to simulate the real data, here we establish two different types of fractional order (Caputo and Caputo–Fabrizio) COVID-19 models with distributed time-delay. Parameters are estimated by the least-square method according to the report data of China and other 12 countries. The results of Caputo and Caputo–Fabrizio model with distributed time-delay and without delay, the integer-order model with distributed delay are compared. These show that the fractional-order model can be better in fitting the real data. Moreover, Caputo order is better in short-term time fitting, Caputo–Fabrizio order is better in long-term fitting and prediction. Finally, the influence of several parameters is simulated in Caputo order model, which further verifies the importance of taking strict quarantine measures and paying close attention to the incubation period population.

scholarly journals Media/Psychological Impact on Multiple Outbreaks of Emerging Infectious Diseases

2007 ◽  
Vol 8 (3) ◽  
pp. 153-164 ◽  
Author(s):  
Rongsong Liu ◽  
Jianhong Wu ◽  
Huaiping Zhu
Keyword(s):  
Infectious Diseases ◽  
Compartmental Model ◽  
Psychological Impact ◽  
Emerging Infectious Diseases ◽  
Transmission Dynamics ◽  
Periodic Oscillations ◽  
Nonlinear Incidence ◽  
Incidence Function ◽  
Contact Patterns ◽  
Nonlinear Incidence Function

We use a compartmental model to illustrate a possible mechanism for multiple outbreaks or even sustained periodic oscillations of emerging infectious diseases due to the psychological impact of the reported numbers of infectious and hospitalized individuals. This impact leads to the change of avoidance and contact patterns at both individual and community levels, and incorporating this impact using a simple nonlinear incidence function into the model shows qualitative differences of the transmission dynamics.

scholarly journals The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Salih Djilali ◽  
Behzad Ghanbari
Keyword(s):  
Infectious Disease ◽  
Fractional Order ◽  
Graphical Representation ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Hunting Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Interaction ◽  
The Stability

AbstractIn this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate their activities as part of their hunting behavior in order to improve their chances of making a kill and feeding. In this model, we then shift the role of standard derivatives to fractional-order derivatives to take advantage of the valuable benefits of this class of derivatives. Moreover, the stability of equilibrium points is studied. The influence of this infection measured by the transmission rate on the evolution of predator-prey interaction is determined. Many scenarios are obtained, which implies the richness of the suggested model and the importance of this study. The graphical representation of the mathematical results is provided through a precise numerical scheme. This technique enables us to approximate other related models including fractional-derivative operators with high accuracy and efficiency.

scholarly journals Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

2021 ◽  
pp. 104953
Author(s):  
Salih Djilali ◽  
Soufiane Bentout ◽  
Tarik Mohammed Touaoula ◽  
Abdessamad Tridane ◽  
Sunil Kumar
Keyword(s):  
Epidemic Model ◽  
Distributed Delay ◽  
Global Behavior ◽  
Nonlinear Incidence ◽  
Incidence Function ◽  
Nonlinear Incidence Function

scholarly journals Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 238
Author(s):  
Ricardo Almeida ◽  
Natália Martins ◽  
Cristiana J. Silva
Keyword(s):  
Global Stability ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Epidemiological Models ◽  
Order Model ◽  
Globally Asymptotically Stable ◽  
Incidence Function ◽  
Sirs Model ◽  
Fractional Differential ◽  
Disease Free

In this paper, we present a new result that allows for studying the global stability of the disease-free equilibrium point when the basic reproduction number is less than 1, in the fractional calculus context. The method only involves basic linear algebra and can be easily applied to study global asymptotic stability. After proving some auxiliary lemmas involving the Mittag–Leffler function, we present the main result of the paper. Under some assumptions, we prove that the disease-free equilibrium point of a fractional differential system is globally asymptotically stable. We then exemplify the procedure with some epidemiological models: a fractional-order SEIR model with classical incidence function, a fractional-order SIRS model with a general incidence function, and a fractional-order model for HIV/AIDS.

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