Integration of epidemic diffusion and adjacent edge properties to outbreak management model

Infectious diseases and epidemics pose a universal threat to humanity. A variety of closed loop pharmaceutical supply-chain management models and network models were studied intensively in the recent years. Recent development in epidemic modelling continues to assert the precision of information in accordance to time. Yet in the context of epidemics, the number of infectants are not pre-determined, so is the demand function of the mathematical model. The proposed model employs a multi-period nonlinear mixed integer programming (MINLP) optimization model to a three-echelon supply chain model to address three main research gaps. The first is the nonlinear nature of population demand. The number of infectants of tomorrow is dictated by the number of infectants of yesterday, and the infected of today. The second is the interaction between populations. Literature disregarded that an infectant may be infected due to the interaction (incoming and outgoing) between two populations. Third, the proposed model extends by integrating pharmaceutical resource allocation model with non-pharmaceutical network node and link removal in order to combat the progression of an epidemic outbreak. With these, one notable constraint of this study is the population coupling constraint, which dynamically adjust to the condition of the population. The number of infected, susceptible, and recovered affects the demand function constraint. Interestingly, number of infected, susceptible, and recovered adjust in every period; hence, the demand function. An important finding through the study is the existence of nonlinear inverse relationship for trade-offs between the health objective and cost objective. By analyzing different pay-off for health as a main objective, or for economic cost as the main objectives, while satisfying the feasibility condition of the mathematical model, the results presented a range of solution sets for different risk appetites of the decision makers