Optimal control for the spread of infectious disease: The role of awareness programs by media and antiviral treatment

Abstract

SummaryThis paper presents a detailed mathematical analysis of the role of awareness programs by media and antiviral treatment on the control of infectious diseases. A nonlinear model is proposed in order to control the infectious diseases, and the model is examined under various scenarios of control measures using variety of mathematical techniques including stability, sensitivity, optimal control, and cost‐effectiveness analysis. Considering the constant control parameters, the basic reproduction number is derived and investigated by the existence and stability of equilibria, then the relative impact of each of the constant control parameters are assessed by calculating the sensitivity index of the basic reproduction number. Under the time‐dependent controls, the necessary conditions for the optimal control of the disease are derived using the Pontryagin's maximum principle in order to determine optimal strategies for controlling the spread of the disease. In order to investigate the most cost‐effective control strategy among all the possible strategies, cost‐effectiveness analysis is carried out using numerical simulations and the result reveals that the strategy combination of 3 control measures (the successful campaign of awareness programs by media, controlling effort that alters infectious cases receiving treatment, and strengthening effort made on awareness campaign programs) is the most cost‐effective control strategy and this indicates that implementation of all the 3 control measures is necessary in order to control the disease outbreak.