Optimal control of a delayed SIRC epidemic model with saturated incidence rate

2018 ◽  
Vol 40 (2) ◽  
pp. 367-374 ◽  
Author(s):  
Lele Li ◽  
Caixia Sun ◽  
Jianwen Jia
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

scholarly journals Optimal control of an epidemic model with a saturated incidence rate

2012 ◽  
Vol 17 (4) ◽  
pp. 448-459 ◽  
Author(s):  
Hassan Laarabi ◽  
El Houssine Labriji ◽  
Mostafa Rachik ◽  
Abdelilah Kaddar
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Control Framework ◽  
Adjoint Variables ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

In this study we consider a mathematical model of an SIR epidemic model with a saturated incidence rate. We used the optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. The existence result was discussed. A characterization of the optimal control via adjoint variables was established. We obtained an optimality system that we sought to solve numerically by a competitive Gauss–Seidel like implicit difference method.

scholarly journals Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

2020 ◽  
pp. 8-19
Author(s):  
Laid Chahrazed
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability ◽  
Disease Free ◽  
Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

Dynamical Analysis of Salmonella Epidemic Model With Saturated Incidence Rate

2021 ◽  
pp. 545-560
Author(s):  
Abiodun Oluwakemi ◽  
Ibrahim Mohammed ◽  
Adebimpe Olukayode ◽  
Oludoun Olajumoke ◽  
Gbadamosi Babatunde ◽  
...  
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Dynamical Analysis ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

scholarly journals Optimal Control Strategy for a Discrete Time Smoking Model with Specific Saturated Incidence Rate

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Abderrahim Labzai ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Incidence Rate ◽  
Discrete Time ◽  
Control Strategy ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Optimal Control Strategy ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Heavy Smokers

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of smoking with specific saturated incidence rate. The population that we are going to study is divided into five compartments: potential smokers, light smokers, heavy smokers, temporary quitters of smoking, and permanent quitters of smoking. Our objective is to find the best strategy to reduce the number of light smokers, heavy smokers, and temporary quitters of smoking. We use three control strategies which are awareness programs through media and education, treatment, and psychological support with follow-up. Pontryagins maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the performance of the optimization strategy.

Stability analysis of an SVIR epidemic model with non-linear saturated incidence rate

2015 ◽  
Vol 9 ◽  
pp. 1145-1158
Author(s):  
Muhammad Altaf Khan ◽  
Zulfiqar Ali ◽  
L. C. C. Dennis ◽  
Ilyas Khan ◽  
Saeed Islam ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Non Linear ◽  
Saturated Incidence Rate ◽  
Saturated Incidence
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