An HLD Model for Tomato Bacterial Canker Focusing on Epidemics of the Pathogen Due to Cutting by Infected Scissors

Cost-optimal seeding strategy during a botanical pandemic in domesticated fields

Botanical pandemics cause enormous economic damage and food shortages around the globe. However, since botanical pandemics are here to stay in the short-medium term, domesticated field owners can strategically seed their fields to optimize each session's economic profit. In this work, we propose a novel epidemiological-economic mathematical model that describes the economic profit from a field of plants during a botanical pandemic. We describe the epidemiological dynamics using a spatiotemporal extended susceptible-infected-recovered epidemiological model with a non-linear output economic model. We provide an algorithm to obtain an optimal grid-formed seeding strategy to maximize economic profit, given field and pathogen properties. We show that the recovery and basic infection rates have a similar economic influence. Unintuitively, we show that a larger farm does not promise higher economic profit. Our results demonstrate a significant benefit of using the proposed seeding strategy and shed more light on the dynamics of the botanical pandemic.

A PHLID Model for Tomato Bacterial Canker Predicting on Epidemics of the Pathogen

A pathogen, healthy, latently infected, infectious, and diseased plant (PHLID) model for botanical epidemics was defined for tomato bacterial canker (TBC) caused by the pathogenic plant bacteria, Clavibacter michiganensis subsp. michiganensis (Cmm). First, the incubation period had to be defined to develop this type of model. To estimate the parameter of incubation period, inoculation experiments were conducted in which it was assumed that infection is transferred to healthy plants by cutting with contaminated scissors after cutting infected plants with early symptoms or symptomless. The concentration of Cmm was increased over 1 × 10⁶ cells/g plant tissue at 20 cm away from the inoculated point on the stem 10 days after inoculation, and then the approximate incubation period of TBC in symptomless infected plants was defined as 10 days. The developed PHLID model showed the dynamics of diseased plants incidence and fitted the curve of the proportion of diseased plants observed in fields well. This model also contains the factors of pathogen and disease control, and it was able to simulate the control effects and combined two different control methods, which were the soil and scissors disinfections to prevent primary and secondary transmissions, respectively. Thus, this PHLID model for TBC can be used to simulate not only the increasing number of diseased plants but also suppressing disease increase.

Mathematical model of coffee tree's rust control using snails as biological agents

Coffee rust is one of the main diseases that affect coffee plantations worldwide, causing large-scale ecological and economic damage. While multiple methods have been proposed to tackle this challenge, using snails as biological agents have shown to be the most consistent and promising approach. However, snails are an invasive species, and overusing them can cause devastating outcomes. In this paper, we develop and explore an ecological-epidemiological mathematical model for the coffee tree rust pandemic control using snails as biological agents. We analyze the equilibria of the proposed system with their stability properties. In addition, we perform numerical analysis to obtain the sensitivity of the system to different changes and manipulation of the snails pandemic control, under specific conditions. Finally, we propose an in silico mechanism to obtain an analytical connection between the system's initial condition and the number of snails needed to optimally control the rust pandemic spread while preventing the snail population to grow unmanageably. Our model can be used to optimize the usage of snails as biological agents to control the rust pandemic in spatially-small areas, by predicting the number of snails one needs to introduce to the ecosystem in order to obtain a desired outcome.