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Treatment of dynamical nonlinear Measles model: An evolutionary approach | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 134، دوره 13، شماره 1، خرداد 2022، صفحه 1629-1638 اصل مقاله (647.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.20450.2156 | ||
| نویسندگان | ||
| Muhammad Farhan Tabassum1؛ Ali Akgul* 2؛ Sana Akram1؛ Muhammad Farman3؛ Rabia Karim4؛ Saadia Mahmood ul Hassan4 | ||
| 1Department of Mathematics, University of Management and Technology, Lahore, Pakistan | ||
| 2Art and Science Faculty, Department of Mathematics, Siirt University, 56100 Siirt, Turkey | ||
| 3Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan | ||
| 4Department of Sports Sciences, Faculty of Allied Health Science, University of Lahore, Lahore, Pakistan | ||
| تاریخ دریافت: 04 خرداد 1399، تاریخ بازنگری: 09 مرداد 1399، تاریخ پذیرش: 07 مهر 1399 | ||
| چکیده | ||
| Measles is a respiratory system infection caused by a Morbillivirus genus virus. The disease spreads directly or indirectly through respiration from the infected person's nose and mouth after contact with fluids. The vast population of infects in developing countries is yet at risk. Generally, the mathematical model of Measles virus propagation is nonlinear and therefore changeable to solve by traditional analytical and finite difference schemes by processing all properties of the model like boundedness, positivity feasibility. In this paper, an unconditionally convergent semi-analytical approach based on modern Evolutionary computational technique and Padé- Approximation (EPA) has been implemented for the treatment of non-linear Measles model. The convergence solution of EPA scheme on population: susceptible people, infective people, and recovered people have been studied and found to be significant. Eventually, EPA reduces contaminated levels very rapidly and no need to supply step size. A robust and durable solution has been established with the EPA in terms of the relationship between disease-free equilibrium in the population. When comparing the Non-Standard Finite Difference (NSFD) approach, the findings of EPA have shown themselves to be far superior. | ||
| کلیدواژهها | ||
| Optimization؛ Epidemiological Measles Model؛ Padé-approximation؛ Differential Evolution؛ Penalty Function | ||
| مراجع | ||
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[1] L. Allen, M. Jones and C. Martin, A discrete-time model with vaccination for a measles epidemic, Math. Biosci. 105(1) (1991) 111–131. [2] A. Ara, N.A. Khan, O. A. Razzaq, T. Hameed and M.A.Z. Raja, Wavelets optimization method for evaluation of fractional partial differential equations: an application to financial modelling, Adv. Diff. Equ. 2018(1) (2018) 8. [3] J. Brest, S. Greiner, B. Boskovic, M. Mernik and V. Zumer, Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems IEEE Trans. Evol. Comput. 10(6) (2006) 646–657. [4] C.A.C. Coello and E.M. Montes Constraint-handling in genetic algorithms through the use of dominance-based tournament selection, Adv. Eng. Inf. 16(3) (2002) 193–203. [5] K. Ejima, R. Omori, K. Aihara and H. Nishiura, Real-time investigation of measles epidemics with estimate of vaccine efficacy, Int. J. Biol. 8(5) (2012) 620. [6] M. Farman, M.F. Tabassum, M. Saeed and N.A. Chaudhry, Control and simulation impact on nonlinear HepatitisB model by using Pad´e-approximation based differential evolution, (2019), bioRxiv: 831636. [7] B. Grenfell, Chance and chaos in measles dynamics, J. R. Stat. Soc. Ser. B Stat. Meth. 54(2) (1992) 383–398. [8] Z. Kalateh Bojdi, S. Ahmadi-Asl and A. Aminataei, A new extended Pad´e-approximation and its application, Adv. Numerical Anal. 2013 (2013). [9] S. Kumar, A. Ahmadian, R. Kumar, D. Kumar, J. Singh, D. Baleanu and M. Salimi, An efficient numerical method for fractional SIR epidemic model of infectious disease by using Bernstein wavelets, J. Math. 8(4) (2020)558. [10] S. Kumar, R. Kumar, C. Cattani and B. Samet, Chaotic behaviour of fractional predator-prey dynamical system, Chaos, Solitons and Fractals 135 (2020) 109811. [11] S. Kumar, A. Kumar, Z. Odibat, M. Aldhaifallah and K.S. Nisar, comparison study of two modified analytical approach for the solution of nonlinear fractional shallow water equations in fluid flow, AIMS Math. 5(4) (2020) 3035–3055. [12] N. Panagant and S. Bureerat Solving partial differential equations using a new differential evolution algorithm Math. Probl. Eng. 2014 (2014). [13] K. Price, R.M. Storn and J.A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization, Springer Science Business Media, 2006. [14] J. Ochoche and R. Gweryina A mathematical model of measles with vaccination and two phases of infectiousness, IOSR J. Math. 10(1) (2014) 95–105. [15] M. Roberts and M. Tobias Predicting and preventing measles epidemics in New Zealand: application of a mathematical model, Epidem. Infect. 124(2) (2000) 279–287. [16] E. Simons, M. Ferrari, J. Fricks, K. Wannemuehler, A. Anand, A. Burton and P. Strebel, Assessment of the 2010 global measles mortality reduction goal: results from a model of surveillance data, The Lancet. 379(9832) (2012) 2173–2178. [17] M.F. Tabassum, S. Akram, S. Mahmood-ul-Hassan, R. Karim, P.A. Naik, M. Farman and M. H. Ahmad, Differential gradient evolution plus algorithm for constraint optimization problems: A hybrid approach, Int. J. Optim. Control Theory Appl. 11(2) (2021) 158–177. [18] M.F. Tabassum, M. Farman, P.A. Naik, A. Ahmad, A.S. Ahmad and H. Saadia, Modeling and simulation of glucose-insulin glucagon algorithm for artificial pancreas to control the diabetes mellitus, Network Model. Anal. Health Inf. Bioinf. 10(1) (2021) 1–8. [19] M.F. Tabassum, M. Saeed, N. Ahmad, A. Sana and N. Riaz, Solution of war planning problem using derivative-free methods, Sci. Int. 27(1) (2015) 395–398. [20] M.F. Tabassum, M. Saeed, A. Akg¨ul, M. Farman and S. Akram, Solution of chemical dynamic optimization systems using novel differential gradient evolution algorithm, Phys. Scr. 96(3) (2021) 035212. [21] M.F. Tabassum, M. Saeed, A. Akg¨ul, M. Farman and N.A. Chaudhry, Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Pad´e-approximation, Chaos Solitons Fractals 134 (2020) 109686. [22] M. Tabassum, M. Saeed, N.A. Chaudary, J. Ali and A. Sana, Integrated approach of set theory and pattern search methods for solving aircraft attacking problem, Pak. J. Sci. 69(1) (2017) 136–143. [23] M.F. Tabassum, M. Saeed, N.A. Chaudhry and S. Akram, Treatment of non-linear epidemiological smoking model using evolutionary Pad´e-approximation: Treatment of non-linear smoking model using EPA, Proc. Pakistan Acad. Sci. 57(2) (2020) 11–19. [24] M. F. Tabassum, M. Saeed, N.A. Chaudhry, J. Ali and M. Farman, S. Akram, Evolutionary simplex adaptive Hooke-Jeeves algorithm for economic load dispatch problem considering valve point loading effects, Ain Shams Eng. J. 12(1) (2021) 1001–1015. [25] M.F. Tabassum, M. Saeed, N. Chaudhry, A. Sana and Z. Zafar, Optimal design of oxygen production system by pattern search methods, Pak. J. Sci. 67(4) (2015) 371–376. [26] M.F. Tabassum, M. Saeed, A. Sana and N. Ahmad, Solution of 7 bar tress model using derivative-free methods Proc. Pakistan Acad. Sci. 52(3) (2015) 265–271. [27] M. Vajta, Some remarks on Pad´e-approximations, Proc. 3rd TEMPUS-INTCOM Symposium, 2000. [28] World Health Organization, Global measles and rubella strategic plan, 2012. | ||
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