MODELING THE TRANSMISSION DYNAMICS OF TWO STRAINS COVID-19 WITH OPTIMAL CONTROL STRATEGIES FOR ITS SPREAD

This thesis presents a comprehensive mathematical modeling framework to assess and optimize control strategies for the transmission dynamics of two co-circulating strains SARS-CoV-2 in Nigeria, with a specific focus on the original and Delta variants. Leveraging compartmental modeling and optimal control theory, the study formulates a deterministic
model comprising susceptible, exposed, infected, hospitalized, recovered, and vaccinated compartments, further disaggregated by strain type. The model incorporates time-dependent control measures, namely preventive efforts, vaccination, and treatment
interventions, aimed at mitigating infection spread and associated costs. The model analysis begins with theoretical validation, including positivity and boundedness of the model solution, derivation of disease-free and endemic equilibria. Basic reproduction numbers for each strain of the infection are computed using the next-generation matrix approach, serving as thresholds for disease persistence or elimination. Stability analyses are conducted to characterize the conditions under which the virus can be eradicated. The model exhibits backward bifurcation under certain parameter, emphasizing the necessity
for rigorous control efforts even when reproduction numbers are below unity. Optimal control strategies are derived using Pontryagin’s Maximum Principle, leading to a system of coupled differential equations comprising the state and adjoint variables. The forward-backward sweep method is implemented in MATLAB to numerically simulate the optimal trajectories under various scenarios. Sensitivity analyses is conducted to identify the most influential parameters, guiding policy decisions. Numerical results reveal that a combined strategy incorporating prevention, vaccination, and treatment is
most effective in reducing infection prevalence and the overall cost of intervention.