Renewal Equations Applied to Evaluation of Interventions for the Control and Prevention of Infectious Diseases

Control and prevention of infectious disease prevalence have been a priority to reduce the burden (mortality and morbidity) of the diseases. Mathematical modeling has been used to study the direct and indirect effect of Infection Prevention and Control (IPC) measures on the disease transmission dynamics and to estimate the cost effectiveness of immunization programs including vaccine production and immunization program design and implementation. However, for more efficient programs regarding IPC priority policies and in order to optimize the limited available resources for the control of infectious diseases, more rigorous mathematical models and analyses are required. This dissertation is dedicated to the development of a mathematical framework using delay systems (delay/functional differential equations and Volterra integral equations of second type) to examine the effectiveness of control and prevention interventions for infectious diseases. The framework enables us to formulate and derive mathematical and epidemiological analyses of a wide range of compartmental models that have been traditionally studied using ordinary, partial and delay differential equations. We specifically use this framework to address heterogeneity in the population and to better understand the disease dynamics and the burden of the disease with and without interventions. We also use this framework to study vertical transmission and vector-borne diseases.