Abstract:
In this thesis a Mathematical models for transmission dynamics of Potato leaf roll virus using integer and fractional order differential equation are developed. The models considered Potato as well as Vector populations. The potato populations is sub-divided in to two compartments namely, susceptible potato and infected potato. Similarly the vector population is also sub-divided into susceptible vector and infected vector. First we developed the integer order of potato leaf roll virus model and then transform it in to fractional order due to the reason that, fractional order possess memory and other benefit in modeling of real life phenomena. Secondly the invariant region, positivity of future solution, equilibrium points and stabilities condition of equilibrium states of the model are analyzed in both approaches to determine the qualitative behaviors of the model. The basic reproduction number of the model also established. The result showed that the disease free equilibrium is locally and globally stabile whenever basic reproduction number is less than one. On the other hand endemic equilibrium is stabile if basic reproduction number is greater than one. Finally the numerical simulation of the model are performed in both integer and fractional order using MATLAB computer program to support the analytical solution and to investigate the effect of each parameter on the control of the disease. To perform this numerical simulation, the value of parameters and state variables of the model are collected from relevant documents and some of them are assumed. The results obtained from numerical simulation indicate that elimination rate of infected potato and contact rate have a great contribution in combating potato leaf roll virus.
