GEOSPATIAL MATHEMATICAL MODELING OF DISEASE HOTSPOTS USING PARTIAL DIFFERENTIAL EQUATIONS

What if mathematical models could forecast disease hotspots as precisely as weather maps? This study applied geospatial mathematical modeling using Partial Differential Equations (PDEs) to predict disease hotspot accuracy across Ghana from 2020 to 2024-an innovation vital for epidemic control where traditional surveillance lags. The objective was to assess how PDE modeling components and geospatial data integrity affect hotspot prediction performance. A total of 105 observations were drawn from secondary datasets provided by the Ghana Health Service, WHO, and GIS platforms. Descriptive statistics, correlation matrices, and regression analyses were conducted. Results showed true positive detection rates averaging 87%, centroid errors within 2.5 km, and predictive reliability indices reaching 0.79. Model Validation Techniques showed the strongest influence on prediction accuracy (β = -0.136; p = 0.088), while overall model variance explained was low (R² = 0.017), and the strongest correlation coefficient was r = -0.117. Nonetheless, high-resolution grids improved prediction accuracy by up to 15.1 percentage points and DEM-adjusted forecasts reduced spatial error by 1.4 cases per 1,000. The study concludes that PDEs offer practical, high-fidelity epidemic forecasts when supported by spatial resolution optimization and improved data integrity. Recommendations include expanding real-time GIS inputs, refining PDE algorithms for rural zones, and investing in infrastructure that supports mobile-based surveillance feedback.