Original Contributions to the Theory of Nonlinear Control of Epidemic Spread on Complex Networks with Application to Nigerian Public Health Systems

The control of epidemic processes on heterogeneous contact networks is a fundamental challenge in mathematical epidemiology, with direct implications for the design of optimal intervention strategies in the complex social and institutional networks that characterise Nigerian public health systems. This dissertation makes three original theoretical contributions. First, it develops a degree-based mean field model for epidemic spread on configuration model random graphs with heterogeneous degree distributions calibrated to contact network data from Ibadan, Lagos, and Kano urban centres. Second, it proves novel sufficient conditions for global asymptotic stability of the disease-free equilibrium on heterogeneous networks using a Lyapunov function constructed from the network spectral radius, generalising existing results applicable only to homogeneous mixing models. Third, it formulates and solves an optimal control problem on the network epidemic model, deriving necessary conditions for the time-optimal intervention strategy using Pontryagin's Maximum Principle adapted to the network state dimension. Numerical implementation using adjoint-based gradient descent is demonstrated for measles control scenarios in the Kano metropolitan contact network, showing that targeted vaccination of high-degree nodes achieves herd immunity threshold with 34 percent lower total doses than uniform population vaccination. The theoretical framework is validated against retrospective epidemic data from the 2017 meningitis outbreak in North West Nigeria. Keywords: network epidemic control, optimal control theory, Pontryagin's principle, complex networks, global stability.