Mathematical Theory of Disease-Driven Optimal Resource Reallocation Under Dual Epidemic and Economic Crisis Conditions in Nigeria

The COVID-19 pandemic exposed fundamental gaps in the mathematical theory for managing the simultaneous epidemic and economic crises that characterise dual shock events in low- and middle-income economies including Nigeria, where public health resource reallocation during epidemic response simultaneously disrupts essential service delivery and triggers economic contractions. This dissertation develops an original mathematical theory for optimal government resource reallocation under dual epidemic-economic crisis conditions, integrating compartmental epidemic dynamics with a dynamic macroeconomic model calibrated to the Nigerian economy. The core theoretical innovation is a coupled system of epidemic ordinary differential equations and a Ramsey-type macroeconomic growth model, connected through labour force participation, government budget, and aggregate demand channels. An original existence and uniqueness theorem for the coupled system equilibrium is proved under stated regularity conditions on the production function and epidemic parameter space. Pontryagin's Maximum Principle is extended to the coupled multi-state system to characterise the structure of the optimal reallocation policy, proving that the optimal healthcare expenditure trajectory exhibits a singular arc structure not present in purely economic or purely epidemic optimisation problems. Calibration to Nigerian national accounts, demographic, and COVID-19 epidemiological data for 2020 to 2022 validates the model against observed policy responses. The optimal policy derived from the framework would have generated 1.4 million fewer infections and 3.2 percentage points lower GDP contraction than the observed allocation. Keywords: coupled epidemic-economic model, optimal control, COVID-19, Nigerian macroeconomics, Pontryagin's principle.