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Journals / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2022 / Cilt: 12 - Sayı: 2

Nonstandard Discretization and Stability Analysis of a novel type Malaria-Ross Model

Mehmet KOCABIYIK
Pages
1023–1033
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, the findings are expressed with graphs and tables.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Malaria is still a deadly disease in most developing countries.
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Key Findings & Data:In order to prevent this and many other diseases in all countries, it is necessary to understand the dynamics of the disease well.
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Conclusion & Impact:Finally, the findings are expressed with graphs and tables.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Distributed order differential equations · Malaria-Ross model · numerical Analysis

Abstract

Malaria is still a deadly disease in most developing countries. In order to prevent this and many other diseases in all countries, it is necessary to understand the dynamics of the disease well. For this reason, in this study, a new type of Malaria-Ross equation, Distributed order, is discussed. In this new type, the dynamics of the disease can be understood better and quicker in different situations with the density function included in such equations. Numerical discretization of this model is done with the help of a nonstandard finite difference scheme. Afterward, stability analyses of the equilibrium points obtained from the model that were performed. At the same time, comparisons were made with other numerical methods. Finally, the findings are expressed with graphs and tables.

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Cite This Article

KOCABIYIK, M. (2022). Nonstandard Discretization and Stability Analysis of a novel type Malaria-Ross Model. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 12 - Sayı: 2, 1023–1033. https://ajindex.com/articles/538449

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References (8)

  1. Aminikhah H, Refahi A, Rezazadeh H, 2013. Stability analysis of distributed order fractional Chen system. The Scientific World Journal, 2013.
  2. Anderson RM, May RM, 1991. Infectious diseases of humans: dynamics and control London: Oxford University Press. Aron JL, 1988. Mathematical modeling of immunity to malaria. Math Bioscience, 90: 385-396.
  3. Aron JL, May RM, 1982. The population dynamics of malaria. In Population Dynamics of Infectious Disease. Edited by: Anderson RM. London: Chapmanand Hall, pp. 139-179.
  4. Bagley RL, Torvik PJ, 2000 a. On the existence of the order domain and the solution of distributed order equations-Part I. International Journal of Applied Mathematics, 2(7): 865-882.
  5. Bagley RL, Torvik PJ, 2000b. On the existence of the order domain and the solution of distributed order equations-Part II. International Journal of Applied Mathematics, 2(8): 965-988. Caputo M, 1969. Elasticita e dissipazione. Zanichelli. Caputo M, 1995. Mean fractional-order-derivatives differential equations and filters. Annali dell’Universita di Ferrara, 41(1): 73-84. Caputo M, 2001. Distributed order differential equations modelling dielectric induction and diffusion. Fractional Calculus and Applied Analysis, 4(4): 421-442. Caputo M, 2003. Diffusion with space memory modelled with distributed order space fractional differential equations. Annals of Geophysics. Chitnis N, 2005. Using mathematical models in controlling the spread of malaria. PhD thesis University of Arizona, Program in Applied Mathematics. Diethelm K, Ford NJ, 2009. Numerical analysis for distributed-order differential equations. Journal of Computational and Applied Mathematics, 225(1): 96-104. Dietz K, 1988. Mathematical models for transmission and control of malaria. In Principles and Practice of Malariology. Edited by: Wernsdorfer W, McGregor Y. Edinburgh: Churchill Livingston, pp. 1091-1133.
  6. Dimitrov DT, Kojouharov HV, 2007. Nonstandard numerical methods for a class of predator-prey models with predator interference. Electronic Journal of Differential Equations (EJDE) pp. 67-75.
  7. Dimitrov DT, Kojouharov HV, 2008. Nonstandard finite-difference methods for predator–prey models with general functional response. Mathematics and Computers in Simulation, 78(1): 1-11. Dorciak L, 1994. Numerical models for simulation the fractional-order control systems, UEF-04-94,
  8. The Academy of Sciences, Institute of Experimental Physic, Kosiice, Slovak Republic. Elsheikh S, Ouifki R, Patidar KC, 2014. A non-standard finite