Stability analysis of fractional order SEIR model for malaria disease in Khyber Pakhtunkhwa

• Autorzy: Badshah Noor , Akbar Haji

Identyfikatory

DOI

10.1515/dema-2021-0029

• Języki publikacji: EN

Abstrakty

EN

We discussed stability analysis of susceptible-exposed-infectious-removed (SEIR) model for malaria disease through fractional order and check that malaria is epidemic or endemic in Khyber Pakhtunkhwa (Pakistan). We show that the model has two types of equilibrium points and check their stability through Routh-Hurwitz criterion. We find basic reproductive number using next-generation method. Finally, numerical simulations are also presented.

Słowa kluczowe

EN

SEIR model; fractional order; Routh-Hurwitz criterion; next-generation method

PL

SEIR; rząd niecałkowity; kryterium stabilności Routha-Hurwitza; sekwencjonowanie nowej generacji

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 326--334
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Badshah Noor

• Department of Basic Sciences and Islaimiat, University of Engineering and Technology Peshawar, Peshawar, Pakistan

autor

Akbar Haji

• Department of Basic Sciences and Islaimiat, University of Engineering and Technology Peshawar, Peshawar, Pakistan

Bibliografia

• [1] C. M. A. Pinto and J. A. Tenreiro Machado, Fractional model for malaria transmission under control strategies, Comput. Math. Appl. 66 (2013), no. 5, 908–916.
• [2] R. Almeida, Analysis of a fractional SEIR model with treatment, Appl. Math. Lett. 84 (2018), 56 –62.
• [3] M. Trawicki, Deterministic seirs epidemic model for modeling vital dynamics, vaccinations, and temporary immunity, Mathematics 5 (2017), no. 1, 7, DOI: https://doi.org/10.3390/math5010007.
• [4] S. Javeed, S. Anjum, K. Saleem Alimgeer, M. Atif, M. S. Khan, W. A. Farooq, et al., A novel mathematical model for COVID-19 with remedial strategies, Results Phys. 27 (2021), 104248, DOI: https://doi.org/10.1016/j.rinp.2021.104248.
• [5] A. Sohail, M. Iftikhar, R. Arif, H. Ahmad, K. A. Gepreel, and S. Iftikhar, Dengue control measures via cytoplasmic incompatibility and modern programming tools, Results Phys. 21 (2021), 103819, DOI: https://doi.org/10.1016/j.rinp.2021.103819.
• [6] E. Demirici, A. Unal, and N. Ozalp, A fractional order SEIR model with density dependent death rate, Math. Stat. 40 (2011), 287–295.
• [7] F. Al-Basir, A. M. Elaiw, D. Kesh, and P. K. Roy, Optimal control of a fractional-order enzyme kinetic model, Control Cybernet. 44 (2015), no. 4, 443–461.
• [8] Z. Ul Abadin Zafar, K. Rehan, and M. Mushtaq, Fractional-order scheme for bovine babesiosis disease and tick populations, Adv. Difference Equ. 2017 (2017), 86.
• [9] I. Podlubny, Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198, Academic Press, 1998.
• [10] A. Rachah and D. F. M. Torres, Analysis, simulation and optimal control of a SEIR model for Ebola virus with demographic effects, arXiv:http://arXiv.org/abs/arXiv:1705.01079 (2017).
• [11] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), no. 1–2, 29–48.
• [12] R. Garrappa, Numerical solution of fractional differential equations: A survey and a software tutorial, Mathematics 6 (2018), no. 2, 16, DOI: https://doi.org/10.3390/math6020016.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).