By PhD candidate Marta Corbetta, with the contribution of Prof. Tito Caffi, Dr. Carlotta Lomeo and Prof. Vittorio Rossi | UCSC
Evolution of the context
Pest management undergone several seasons of changes. By the end of the 20th century, there was an important shift from calendar-based method to integrated pest management (IPM), which requires specialised expertise and technical knowledge. For this reason, the dissemination of all available IPM techniques, including the use of mathematical models, was endorsed by technical supports that have evolved over time from direct to indirect technical assistance, as the techniques gradually became more based on new Information and Communication Technologies (ICT).
IPM aligns with broader goals such as the European Green Deal, which seeks to reduce net greenhouse gas emissions by at least 55% by 2030, even through the reduction of the use of plant protection products by 50%.
Mathematical Models
Mathematical models play a crucial role in the management of pests, i.e. any species, strain or biotype of plant, animal or pathogenic agent injurious to plants or plant products (IPPC, 2024). In this blogpost, we focus on plant disease models as an example of pest models. Plant disease models are a simplified representation of the relationships between pathogens, crops, and the environment that cause the development of epidemics over time and/or space.
First approaches in plant disease models have been empiric (the so called data-based models), by defining mathematical relationships between the components of the disease cycle (such as infection or sporulation of the pathogen) and concomitant environmental variables (such as air temperature, rainfall, or the duration of wet periods) in a field-collected dataset, through simple rules, graphs, or tables to show the relationships. Although these models have the potential to provide a good representation of a set of observed data, they did not account for underlying biological mechanisms (molecular, biochemical, population, etc.), making them easy to develop, but less reliable and robust in different agricultural contexts.
To address these limitations, process-based (mechanistic) models have been introduced in the 1990s. These models focus on the biological processes of the pathogen, including their developmental stages, and the environmental and cultural factors (phenological stages and susceptibility of the host plant) that influence their development. Mechanistic models are more complex, but offer greater reliability and flexibility compared to empirical models. They help identify risk periods for infection and optimal times for disease control measures.
In the modelling approach of Università Cattolica del Sacro Cuore, Piacenza, Italy, there are four basic steps that have been used for developing several weather-driven, mechanistic plant disease models: i) definition of the model purpose; ii) conceptualization, iii) development of mathematical relationships, and iv) model evaluation (Fig. 1).

Model Validation
All mathematical models must be validated for their ability to correctly interpret biological phenomena and the dynamics of plant diseases. Biological validation consists of comparing, in a variety of crop situations, the output of the model with reality, by using independent data sets (data that were not used for model development).
Models, and particularly process-based models, have widely demonstrated their ability to optimise field monitoring activities and scheduling pest control interventions, both in terms of timing and type of products to be used for each specific intervention.
Decision Support Systems
Mathematical models play a critical role in the management of this complex scenario. Plant disease models must be complemented with other models, such as the ones for crop growth and pesticide dynamics, to provide a comprehensive view of the agroecosystem. This multi-modelling approach can be obtained by using expert systems. Magarey et al. (2002), introduced the figure of the ‘super advisor’, a consultant that incorporates all the management solutions for farmers and provides all the information that helps the user making correct and timely decisions. A multi-modelling approach and the use of expert systems have been implemented into decision support systems (DSSs, Fig. 2) to help farmers solve complex problems while reducing the time and resources needed for analysing the available information and for selecting the best solutions. DSSs have further evolved to provide support not only for crop protection, but for the entire crop system management, with functionalities for fertilisation, irrigation, soil and canopy management, and maturity and yield forecasting.

To this end, DSSs are increasingly integrating various Agriculture 4.0 technologies to capture more and more data on the crop environment. They provide dynamic information throughout the season, with hourly or daily updates, and with reference to individual plots characterised by different varieties (including susceptibility to harmful organisms) and possibly cultivated with different techniques, including plant protection treatments.
Perspectives
It has been widely documented that mathematical models enhance crop protection strategies in agricultural crops. The application of these models has resulted in more strategic placement of treatments, leading to improved effectiveness and fewer interventions. Digital solutions should be regarded not as an alternative to the advice provided by agronomists, but as an aid for technicians and farmers to gain a deeper understanding of agroecosystem conditions, even in real time and from a distance, thus increasing their awareness of crop health and risks, and optimizing agricultural interventions.
STELLA’s approach to modelling
The STELLA Pest Surveillance System (PSS) platform will be developed within the project with the ultimate goal of establishing a centralised system for monitoring diseases and pests across the EU and in New Zealand. In this context, the STELLA project focuses on the threat posed by non-native pests, which have increased in recent decades due to globalization and international trade.

The project aims to develop bioclimatic models to estimate the potential distribution of pest species; these models will be based on indices that assess the risk of specific diseases caused by regulated and quarantine pests, including bacteria, fungi, insects, and phytoplasmas. Through this comprehensive approach, the STELLA project seeks to enhance pest management strategies and reduce the impact of invasive pests on agricultural systems.