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Modelling and analysis of a fractional-order epidemic model incorporating genetic algorithm-based optimization

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Abstract

Infectious diseases have always been a threat to the smooth running of our daily activities. To regulate the disease’s devastating outcome, we have performed a qualitative study of infectious disease using an SIR model. While formulating the model, we have taken into account the saturated incidence function with three controls, namely, treatment control, vaccination control, and media awareness. To make the model more robust, we have updated the model using Caputo fractional-order differential equation. We have determined the existence and uniqueness of the solution along with all possible equilibrium points. We have also obtained the basic reproduction number and the criteria of asymptotic local and global stability, taking the basic reproduction number as the threshold parameter. Finally, to control the disease, we have performed the optimization using a metaheuristic search and optimization technique, genetic algorithm (GA).

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Acknowledgements

The work of S. Adak is supported by Indian Institute of Engineering Science and Technology (IIEST), Shibpur, India (No. 1878/1(5)/Exam, dated: 19th January, 2021), the work of S. Barman is financially supported by National Fellowship for Scheduled Caste Students (UGC-NFSC, UGC-Ref.No.:-191620004584, Dated:-20/05/2020), the work of S. Majee is financially supported by Council of Scientific and Industrial Research (CSIR), India (File No. 08/003(0142)/2020-EMR-I, dated: 18th March, 2020), and the work of T.K. Kar is financially supported by Science and Engineering Research Board (File No. MTR/2022/000734, dated: 19/12/2022), Department of Science and Technology, Government of India. In addition, the authors would like to thank anonymous reviewers and the Editor-in-Chief, Chin-Hong Park for their constructive comments and suggestions to improve the quality and presentation of the manuscript significantly.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal, 711103, India

    Sayani Adak, Snehasis Barman, Suvankar Majee & T. K. Kar

  2. Department of Mathematics, Ramsaday College, Amta, Howrah, West Bengal, 711401, India

    Soovoojeet Jana

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  1. Sayani Adak
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Correspondence to Soovoojeet Jana.

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Appendix A

Appendix A

Algorithm of GA

———————————————————————————-

Input:

Objective function, \(\mathscr {R}_0\)

Constraint function,

Population size, n

Maximum number of iterations, M

Crossover probability,

Mutation probability,

Upper and lower bound of variables

Output:

Global optimal solution \(O_b\).

———————————————————————————- 

begin

Generate initial population randomly containing n chromosomes \(O_i,\)

\((i=1,~2,~3,...,~n)\)

Set iteration t=0;

Determine fitness value;

Check if constraint conditions are met;

while(\(t<M\))

Select pair of chromosomes from initial population based on fitness value;

Apply crossover on selected pair with crossover probability;

Apply mutation on the offspring generated from crossover with mutation

probability;

Replace old population with new population;

Increase iteration t by 1

end while

return the best solution, \(O_b\)

end

———————————————————————————-

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Adak, S., Barman, S., Jana, S. et al. Modelling and analysis of a fractional-order epidemic model incorporating genetic algorithm-based optimization. J. Appl. Math. Comput. 71, 901–925 (2025). https://doi.org/10.1007/s12190-024-02224-y

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