Optimal Control of Plant Disease Epidemics with Clean Seed Usage.

Area of Science:

• Agricultural Science
• Epidemiology
• Mathematical Modeling

Background:

• Plant diseases pose significant threats to food security in developing countries.
• Pathogen-free planting material, or "clean seeds," offers a promising disease control strategy.
• Economic and epidemiological factors influence the effectiveness of clean seed distribution.

Purpose of the Study:

• To determine the optimal usage of clean seeds for minimizing plant disease prevalence.
• To analyze the economic viability of clean seed programs through static and dynamic optimization.
• To identify conditions under which subsidies for clean seeds are effective.

Main Methods:

• Utilized a simple Susceptible-Infected (S-I) epidemiological model.
• Applied static optimization with an economic criterion.
• Employed dynamic optimal control and Pontryagin's maximum principle.

Main Results:

• Disease control outcomes vary based on economic and epidemiological parameters.
• A critical subsidy rate determines the economic viability of clean seed usage.
• Static and dynamic models yield comparable, simplified conditions for optimal control.

Conclusions:

• Subsidizing clean seeds can be an effective strategy for disease eradication or control.
• The critical subsidy rate is consistent across static and dynamic optimization approaches.
• Findings are applicable to managing diseases like maize lethal necrosis in East Africa.