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

Dynamics of a delayed epidemic model with varying immunity period and nonlinear transmission

2015 ◽  
Vol 08 (02) ◽  
pp. 1550027 ◽  
Author(s):  
Aadil Lahrouz
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Incidence Rates ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
The Basic Reproduction Number

An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.

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>

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 Global Stability of a Delayed SIRI Epidemic Model with Nonlinear Incidence

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Amine Bernoussi ◽  
Abdelilah Kaddar ◽  
Said Asserda
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Lasalle Theorem ◽  
Nonlinear Incidence Function ◽  
Disease Free

In this paper we propose the global dynamics of an SIRI epidemic model with latency and a general nonlinear incidence function. The model is based on the susceptible-infective-recovered (SIR) compartmental structure with relapse (SIRI). Sufficient conditions for the global stability of equilibria (the disease-free equilibrium and the endemic equilibrium) are obtained by means of Lyapunov-LaSalle theorem. Also some numerical simulations are given to illustrate this result.

Sign in / Sign up

Export Citation Format

Share Document