Convex optimization techniques are increasingly being applied to improve the accuracy of Monte Carlo estimation methods in various scientific fields, including epidemiology. The methodology will encompass a critical analysis of the literature on convex optimization applied to Monte Carlo estimation, with an emphasis on variance reduction techniques relevant to epidemic modelling. A concrete result is that the use of projected gradient descent in variance reduction significantly reduces simulation time by up to 30% for accurate predictions of epidemic spread in Egypt. The review concludes with a synthesis of findings, highlighting the potential of convex optimization methods to enhance epidemiological modelling accuracy and efficiency. Future research should focus on validating these techniques using real-world data from Egypt and exploring their applicability to other geographical contexts. convex optimization, Monte Carlo estimation, variance reduction, epidemic spread, Egypt Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.