The price of grains like maize and sorghum is subject to significant fluctuations, which can have a significant impact on a country's economy and food security. The aim of the study is to model sorghum and maize price volatility in Nigeria. The data utilized in the study was extracted from World Bank Commodity Price Data (WBCPD), 2022. The data consists of monthly prices in nominal US dollars for maize and sorghum from January 1960 – August 2022. The Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models were utilized for capturing the two-grain price volatility. Two types of conditional heteroscedastic models exist, the first group uses exact functions to control the evolution of , while the second group describes with stochastic equations. It is inferred from the result that inherent uncertainties and fluctuations existed in the prices of maize and sorghum in Nigeria which implies that the price volatility is positive and statistically significant suggesting that historical information and past shocks play a crucial role in determining the volatility observed in the grains. It is recommended that the ARCH, GARCH, EGARCH, TGARCH, PARCH, CGARCH, and IGARCH models should be employed for modeling and managing the volatility of maize and sorghum prices in Nigeria. These models have shown effectiveness in capturing different aspects of volatility, including the impact of past shocks, conditional volatility, asymmetry, and other relevant factors.

Mathematical modeling plays a central role in infectious disease epidemiology, shaping outbreak response strategies and informing public health policy. The COVID-19 pandemic demonstrated the value of these models but also exposed persistent limitations related to data fragility, lack of transparency, limited stakeholder engagement, and insufficient consideration of social and political contexts. Rather than critiquing modeling as a discipline, this perspective argues for a reorientation of infectious disease modeling toward a more responsive, equity-centered, and participatory paradigm. We propose a conceptual framework built on three interrelated principles: adaptability through real-time data integration, transparency via open-source and reproducible practices, and relevance through interdisciplinary and co-produced model design. Drawing on illustrative examples from COVID-19 and dengue control efforts, we highlight how integrating behavioral dynamics, local knowledge, and policy feedback can improve model usefulness and public trust. Reconceptualizing models as dynamic systems of inquiry rather than static forecasting tools can enhance decision-making and promote more equitable and effective responses to future public health emergencies.