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مدل دینامیکی انتقال ویروس در گیاهان با دو تأخیر زمانی
Dynamical Model for Virus Transmission in Plants with Two Time Delays
جبر
alg
مقاله مستقل
Original Manuscript
<div style="text-align: justify;"> <span dir="RTL"><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">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 تأخیر 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</span></span></span> <span dir="RTL"><span style="font-family:B Nazanin;"><span style="font-size:10.0pt;">میشود.</span></span></span></div>
<strong>Introduction</strong><br>
One 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’s immune system.<br>
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 <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image002.gif" width="26" > consisting of mature cells and are susceptible to infection, infected cells <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image004.gif" width="24" > that spread the infection, recovered cells <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image006.gif" width="28" > that are no longer infectious and <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image008.gif" width="28" > are proliferating cells that become susceptible after reaching maturity.<br>
We consider two time delays, <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image010.gif" width="13" > and <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image012.gif" width="14" >, in equations. The proliferating cells have the average maturity time <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image010.gif" width="13" >, after which they are recruited to the susceptible class. <img alt="" height="19" src="file:///C:Users1AppDataLocalTempmsohtmlclip1 1clip_image012.gif" width="14" > is the average time of antiviral effects.<br>
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.<br>
<strong>Material and methods</strong><br>
In 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.<br>
<strong>Results and discussion</strong><br>
We 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.<br>
<strong>Conclusion</strong><br>
The following conclusions were drawn from this research.
<ul>
<li>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.</li>
<li>Theorems show that how we can control the virus to prevent epidemic outbreak.</li>
<li>We plot solution curves for two different plants (organic and non-organic). Solution curves show that how the conditions of plant cells change by changing the parameters.</li>
</ul>
مدل ریاضی, نقطه تعادل, پایداری, انشعابهاف.
رده بندی ریاضی (2010): .37C75, 37H20, 00A71
Mathematical model, Equilibrium point, Stability, Hopf bifurcation.
487
500
http://mmr.khu.ac.ir/browse.php?a_code=A-10-670-1&slc_lang=fa&sid=1
Tayebe
Waezizadeh
طیبه
واعظی زاده
waezizadeh@uk.ac.ir
10031947532846003977
10031947532846003977
Yes
Shahid Bahonar university of Kerman
دانشگاه شهیدباهنر کرمان، دانشکدۀ ریاضی و کامپیوتر، بخش ریاضی محض
Tayebe
Parsaei
طیبه
پارسایی
golestan1989@gmail.com
10031947532846003978
10031947532846003978
No
Shahid Bahonar university of Kerman
دانشگاه شهیدباهنر کرمان، دانشکدۀ ریاضی و کامپیوتر، بخش ریاضی محض
Fereshte
Fourozesh
فرشته
فروزش
frouzesh@bam.ac.ir
10031947532846003979
10031947532846003979
No
Bam university
مجتمع آموزش عالی بم، دانشکدۀ ریاضیات و محاسبات نرم، گروه ریاضی