###### Abstract  
Pharmaceuticals play a critical role in the eradication of infectious diseases. Effective pharmaceutical inventory management is important for controlling epidemics since medical resources such as pharmaceuticals, medical staff, and hospitals are limited. In this study, a novel epidemiological model is proposed to evaluate the resource requirements for pharmaceuticals and is applied to analyze different pharmaceutical inventory management strategies. We formulate the relationship between the number of infected individuals and the risk of infection to account for virus mutation. Evolutionary game theory is integrated into an epidemiological model to represent human behavioral choices. The proposed model can be developed to forecast the demand for pharmaceuticals and analyze how human behavior affects the demand of pharmaceuticals. This study found that making people aware of the risk of disease has a positive impact on both reducing the number of infections and managing the pharmaceutical inventory. The main contribution of this study is to enhance areas of research in pharmaceutical inventory management. This study revealed that the correct recognition of the risk of disease leads to appropriate pharmaceutical management. There are a few studies on the application of infectious disease models to inventory control problems. This study provides clues toward proper pharmaceutical management. inventory management; SEIR model; evolutionary game theory +
Footnote †: journal: Medical  
problems and social dilemmas that arise during a pandemic [6]. The SIR model is the most basic model of infectious diseases. This model considers three states: susceptible, infected, and recovered. The SIR model describes changes in these states over time. The SEIR model is extended to include the incubation period state. Other models that take into account the effects of antibodies from vaccination, severity of symptoms, births, deaths, and age have also been studied [7; 8; 9; 10]. Thus, by extending the model to take disease characteristics into account, it is possible to create a model that more closely resembles real-world situations. Research has also been conducted to incorporate not only the characteristics of the disease but also the behavior and intentions of people into the model. Some studies have used game theory to take into account people's fertility rates, to express whether they are vaccinated or not, or to consider two strategies: vaccination and social distance [11; 12]. Studies considering the effect of lockdown policies on the number of infected people [13], the effect of wearing masks [14], and the effect of vaccination on infection rates [15; 16] have been conducted using evolutionary game theory. [PERSON] et al. [17] used evolutionary game theory to express the relationship between human behavior and the prevalence of infectious diseases using the SIR model. Evolutionary game theory is one of the areas of game theory that studies organisms and human behavior based on the idea of biological evolution. The motivation is that, by using game theory, it is possible to express the probability that people change their strategy. This allows us to represent human behavior in a model of infectious diseases. One of the characteristics of COVID-19 is a propensity for recurring cycles of population-wide infections. As shown in Figure 1, the number of infected people has exhibited undulating patterns of growth and decline. Although it is difficult to capture this pattern of infection using the SIR model or SEIR model, the application of evolutionary game theory offers a viable approach to depicting the undulating rise and fall in the number of infected persons [18]. In their study, agents choose whether to voluntarily refrain from going out to reduce the risk of infection and keep themselves quarantined at home or to behave as they would under normal circumstances. The agent decides which strategy to adopt, taking into account the risk of disease transmission and the various costs of self-isolation.