Mathematical modeling of climate change impacts on maize yields in Kenya

Climate change continues to risk maize production in Kenya, yet most of the current modeling approaches evaluate climate variables independently and greatly disregard their interaction with soil fertility. This study addresses this gap by creating a deterministic model that clearly incorporates atmospheric CO₂ concentration, temperature, precipitation, soil fertility (nitrogen), and maize yield into a single time-dependent system. Mathematical analysis is performed to establish the existence of the system’s equilibrium points, providing the necessary conditions for their local and global stability. The analytical results of this study are examined using numerical simulations with MATLAB R2024a using data obtained from the literature and online agricultural and climate databases. Numerical simulations reveal that high levels of CO₂ concentration are associated with increased temperature and precipitation, which accelerate soil nutrient exhaustion and contribute to a yield reduction of approximately 10% under high CO₂ sensitivity. The sensitivity analysis of the major parameters ( β c, β ₐ,\, and\, β ᵣ) further proves that temperature and precipitation responses can increase maize yield by 5–10%, whereas soil fertility serves as one of the primary resilience factors that cushion the negative impacts of climate. These findings show that models excluding soil–climate feedbacks may underestimate long-term productivity risks. The policy implications of the findings are that integrated soil fertility management, climate-resistant varieties of maize, and adaptive water management should be prioritized as major elements of contributing to climate-smart agriculture initiatives that can improve maize productivity and food security in Kenya.