Plant diseases are responsible for 14.1% the world crop loses which represent 220 billion dollars. These phytopathological damages imply several others problems in different sectors concerning human health, the environment and some social and economic aspects of our life (Agrios, 2005). In order to have an efficient solutions to control the causal agents of these diseases it is very important to understand the mechanism of these illnesses very well (Royle and Ostry, 1995; Jeger, 2004).
In phytopathology, the Mathematical tools used offer models describing the process of the infection (Sieve Maanen and Xu, 20033). These mathematical models allow to describe the pathological processes and therefore to foresee the most efficient control methods. The mainly mathematical tools used to model the plant diseases are: Disease progress curves, Linked Differential Equation (LDE) and Area Under disease Progress Curve (AUDPC). Statistical analyses are also employed in the studies of epidemiology of plant diseases. Each tool is utilized for an acute appropriate purpose to model some aspects of the disease development.
The specificity of the host-parasite relationships determine the variables and the adequate mathematical model to be used. On the basis of these chosen mathematical tools the most Known model developed in the phyotopathological studies are: Monomolecular, Exponential, Gompertz and Logistic models. The logistic model which was proposed firstly by Veshulst in 1838 to represent human population growth was after developed by Van der Plank (1963), to being more appropriate for most polycyclic diseases. This growth model is the most widely used for describing epidemics of plant disease (Segarra et al., 2001; Jeger, 2004).
Using the logistic model alone or combined with others tools many plant diseases were described. In the case of the Citrus disease "Mal secco", there is no reports referring to the development of a model allowing to test the resistance degree of the susceptible infected host plants. The causal agent of the "Mal secco"Phoma tracheiphila (Petri) [Kanc et Ghik] is responsible of many important losses in the Citrus crop orchards and it is the most destructive fungal disease of lemon plantation worldwide (O. Gulsen and al, 2006). As fungicides treatments showed non efficient results to control this pathogen, the research of resisting cultivars remains the most efficient solution to decrease the losses inflicted by the pathogen (Solel and Salerno, 1988).
The mathematical survey of the different studied cultivars, using a polynomial model, permits to describe the resistance state of the infected plants. The polynomial interpolation at 5 degrees appears to be the most adequate for this mathematical model. Comparison of R-squared values showed that the polynomial regression at the 5 degree gives the best results. The statistical analysis confirms those obtained by the polynomial model. This polynomial model have the advantage to give a strict evaluation of the state of the resistance of the cultivar tested and not a relative estimation as its in the case of the different mathematical and statistical others classic tools usually used to evaluate the state of the plant resistance. A bio-software based on this polynomial model is developed as an informatic tool of decision to discriminate the resistance level of the tested plant infected by the pathogenic agent.