Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates

The control of highly contagious diseases is very important today. In this paper, we proposed an SEIR model with Crowley–Martin-type incidence rate and Holling type II and III treatment rates. Dynamics of the spread of infection and its control are performed for both the cases of treatment functions...

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Bibliographic Details
Published in:Nonlinear dynamics 2019-06, Vol.96 (4), p.2351-2368
Main Authors: Upadhyay, Ranjit Kumar, Pal, Ashok Kumar, Kumari, Sangeeta, Roy, Parimita
Format: Article
Language:English
Subjects:
Applied mathematics
Automotive Engineering
Cholera
Classical Mechanics
Control
Disease control
Dynamical Systems
Engineering
Epidemics
Epidemiology
Health services
Infections
Infectious diseases
Mathematical models
Maximum principle
Measles
Mechanical Engineering
Optimal control
Original Paper
Parameter sensitivity
Sensitivity analysis
Simulation
Stability analysis
Vibration
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Summary:The control of highly contagious diseases is very important today. In this paper, we proposed an SEIR model with Crowley–Martin-type incidence rate and Holling type II and III treatment rates. Dynamics of the spread of infection and its control are performed for both the cases of treatment functions. We have performed the stability and bifurcation analyses of the model system. The sensitivity analysis of all the parameters with respect to the basic reproduction number has been performed. Furthermore, we discussed the optimal control strategy using Pontryagin’s maximum principle and determined the effect of control parameter u on the model dynamics. Moreover, we validate the theoretical results using numerical simulations. Between both the treatment functions, we observe that the implementation of Holling type II treatment is most effective to prevent the spread of diseases. Thus, we conclude that the pervasive effect of treatment not only reduces the basic reproduction number as the control parameter u increases with nonlinear treatment, h ( I ) but also controls the spread of disease infection among the population.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-04926-6