Development of equation to estimate basic reproduction number of plant disease in case of different host distribution

Abstract

Distribution of susceptible host between agricultural fields is a factor that effect to plant epidemic. The plant epidemic can be described by the basic reproduction number. From its definition, the high value of basic reproduction number can represent high epidemic. The equation is developed to estimate the basic reproduction number to represent the epidemic. To develop the equation, four factors such as the number of spore that the infected host can produce in the infected period, the probability that healthy host become infected host when it receive spore, the probability that the spore land in the distance r and the distribution of susceptible host are considered. Then, Checking the developed equation by using stochastic process. Because the difficulty of real data. The Gillespie’s Algorithm is used to select the event that will happen in stochastic process and consider 180 cases of parameter. The results show that all the correlation coefficient of the basic reproduction number from two method has more than 0.85. that is the basic reproduction number from the developed equation has a very strong relationship with the basic reproduction number from the stochastic process.