Eco-epidemiological model and analysis of potato leaf roll virus using fractional differential equation

• Published in: Arab journal of basic and applied sciences 2021, Vol.28 (1), p.41-50
• Main Authors: Tilahun, Getachew Teshome, Muhammad, Tawfiq, Wolle, Getinet Alemayehu
• Format: Article
• Language: English
• Subjects: Fractional differential equation; modeling; numerical analysis; potato leaf virus
• ISSN: 1815-3852; 2576-5299; 2576-5299
• DOI: 10.1080/25765299.2020.1865621

In this paper, mathematical models for transmission dynamics of Potato leaf roll virus using integer and fractional order differential equations are developed. The models considered Potato as well as Vector populations. The potato population is sub-divided as susceptible (Sp(t)) and infected (Ip(t)). The vector population also sub-divided as susceptible (Sv(t)) and infected (Iv(t)). Firstly, we proposed the integer order of potato leaf roll virus (PLRV) model and then we extend into fractional order due to the reason that fractional order possesses memory and other benefit in modeling of real-life phenomena. Secondly, the qualitative behavior of the model including invariant region, positivity of future solution and equilibrium points are analyzed in both approaches. Finally, numerical simulation is done to investigate the effect of each parameter on the control of the disease for both integer and fractional orders. The results obtained from numerical simulation indicate that increasing elimination rate of infected potato and contact rate have a great contribution in combating potato leaf roll virus in the specified period of time.