______________________________________________________________________Abstract: This paper deals with maintenance service contracts for equipment (such as dump trucks) sold with two dimensional warranties. We consider a situation where an agent offers several maintenance contract options and the owner of the equipment has to select the optimal option. As the availability of the equipment is a critical measure for attaining the owner's business objectives, the maintenance contract options offered need to ensure a high availability of the equipment. We study three maintenance service options considering the availability target from both the owner and OEM point of views and use a non-cooperative game formulation to determine the optimal price structure (i.e., the contract price and repair cost) for the OEM and the optimal contract option for the owner.
In some diseases, due to the restrictive availability of vaccines on the market (e.g., during the early emergence of a new disease that may cause a pandemic such as COVID-19), the use of plasma transfusion is among the available options for handling such a disease. In this study, we developed an SEIR mathematical model of disease transmission dynamics, considering the use of convalescent plasma transfusion (CPT). In this model, we assumed that the effect of CPT increases patient survival or, equivalently, leads to a reduction in the length of stay during an infectious period. We attempted to answer the question of what the effects are of different rates of CPT applications in decreasing the number of infectives at the population level. Herein, we analyzed the model using standard procedures in mathematical epidemiology, i.e., finding the trivial and non-trivial equilibrium points of the system including their stability and their relation to basic and effective reproduction numbers. We showed that, in general, the effects of the application of CPT resulted in a lower peak of infection cases and other epidemiological measures. As a consequence, in the presence of CPT, lowering the height of an infective peak can be regarded as an increase in the number of remaining healthy individuals; thus, the use of CPT may decrease the burden of COVID-19 transmission.
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