Self-financing model for cabbage crops with pest management.

Area of Science:

• Agricultural Economics
• Mathematical Biology
• Ecology

Background:

• Smallholder farmers face financial challenges due to pests reducing crop yields and increasing protection costs.
• Farm profitability is directly linked to a farmer's budget capacity for yield enhancement and pest management.

Purpose of the Study:

• To explore conditions for a sustainable and self-financing cabbage farm.
• To develop and analyze a non-linear mathematical model for cabbage crop economics.

Main Methods:

• A non-linear mathematical model was developed, treating the farm's current account as a dynamic variable.
• The model was analyzed in two parts: without pest management and with a simplified version incorporating pest control.
• Bifurcation analysis was used to understand model dynamics and stability.

Main Results:

• Without pest management, the model identified conditions for budget allocation and showed a double transcritical bifurcation, quantifying yield, income, and pest damage.
• With pest management, a backward bifurcation was observed, indicating complex dynamics.
• Botanical pesticides were identified as a viable strategy for cost-effective pest control.

Conclusions:

• Mathematical modeling provides insights into the economic sustainability of smallholder farms.
• Integrated pest management strategies, like using botanical pesticides, are crucial for maintaining farm viability and profitability.
• The study highlights the importance of financial management and pest control in ensuring self-financing agricultural operations.