مدل دینامیکی انتقال ویروس در گیاهان با دو تاخیر زمانی

در بررسی بیماری‌های ویروسی در گیاهان، واکنش سیستم ایمنی گیاه نقش اساسی ایفا می‌کند. در این مقاله، یک مدل ریاضی، بر اساس دستگاه معادلات دیفرانسیل با تاخیر زمانی برای واکنش سیستم ایمنی گیاه ارائه می‌شود. در ادامه، رفتار دینامیکی مدل حول نقاط تعادل بررسی شده و در پایان، یک گیاه در دو حالت متفاوت اورگانیک و غیراورگانیک در نظر گرفته می‌شود و رفتار منحنی‌های جواب با استفاده از نرم افزارمتلب بررسی می‌شود.

Dynamical Model for Virus Transmission in Plants with Two Time Delays

IntroductionOne of the major challenges in supporting a growing human population is supplies of food. Plants play a major rule in providing human food. Hence, it is important to study plant diseases and provide appropriate models for describing the relationship between plant infection and its growth and reproduction. One of effective models that describes this relationship is mathematical model. One of the important aspects that the mathematical model can presented is the dynamic of the plant rsquo;s immune system.In this paper, a mathematical model for diffusion of infection in the host plant is introduced. The model is based on a differential equation system with two time delays. In this model, the host population of cells is divided into the classes of susceptible cells consisting of mature cells and are susceptible to infection, infected cells that spread the infection, recovered cells that are no longer infectious and are proliferating cells that become susceptible after reaching maturity.We consider two time delays, and , in equations. The proliferating cells have the average maturity time , after which they are recruited to the susceptible class. is the average time of antiviral effects.In the next sections of this paper, stability conditions of equilibrium points are investigated. In the last section, we consider a plant in two different modes, organic and non organic. Then the solution curves are plotted with different time delays and compare solutions together.Material and methodsIn this scheme, first we explain the conditions of plant. Then, a mathematical model with two time delays is introduced. As follows, the dynamical behavior of the model is investigated. At the end of paper, we consider a plant with two different modes and plot the solution curves.Results and discussionWe introduce a mathematical model which explain conditions of plant cells. In this model the independent variable is time, so the model is ODE with two time delays. As follows, using some theorems in dynamical systems, the dynamical behavior of the model is investigated. Using these results, we can provide good conditions for a plant that epidemic does not happen. At the end, we use of Matlab software to plot the solution curves in two different conditions. The curves explain the behavior of plant cells when they are infectious.ConclusionThe following conclusions were drawn from this research.A mathematical model which is introduced in this paper is more realistic than the previous models because, the grow rate of a plant is considered to be logistic.Theorems show that how we can control the virus to prevent epidemic outbreak.We plot solution curves for two different plants (organic and nonorganic). Solution curves show that how the conditions of plant cells change by changing the parameters.