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Depending on a field study for one of the largest iron and paints warehouses in Egypt, this paper presents a new multi-item periodic review inventory model considering the refunding quantity cost. Through this field study, we found that the inventory level is monitored periodically at equal time intervals. Returning a part of the goods that were previously ordered is permitted. Also, a shortage is permissible to occur despite having orders, and it is a combination of the backorder and lost sales. This model has been applied in both crisp and fuzzy environments since the fuzzy case is more suitable for real-life than crisp. The Lagrange multiplier technique is used for solving the restricted mathematical model. Here, the demand is a random variable that follows the normal distribution with zero lead-time. Finally, the model is followed by a real application to clarify the model and prove its efficiency. [ABSTRACT FROM AUTHOR]

This paper presents an optimal control strategy and a cost effectiveness analysis for the Zika virus disease. A mathematical model for the transmission of the Zika virus is considered with four preventive measures as control, namely: the use of treated bednets, the use of condoms, a medical treatment of infected persons, and the use of indoor residual spray (IRS). We obtain the reproduction number R 0 for the disease and carry out a stability analysis. We observe that the disease’s free equilibrium state is stable when R 0 < 1 but unstable when R 0 > 1 , which leads to a spread of the disease. We examine the implementation of various combinations of the possible control strategies in order to determine the most cost-effective one. Based on the computational results, we conclude that a strategy that consists of treated bednets, treatment of symptomatic infected humans and indoor residual spray is the most cost effective strategy. [ABSTRACT FROM AUTHOR]

Zika virus is a flavivirus transmitted to humans primarily through the bite of infected Aedes mosquitoes. In addition to vector-borne spread, however, the virus can also be transmitted through sexual contact. In this paper, we formulate and analyze a new system of ordinary differential equations which incorporates both vector and sexual transmission routes. Theoretical analysis of this model when there is no disease induced mortality shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the associated reproduction number is less than unity and unstable otherwise. However, when we extend this same model to include Zika induced mortality, which have been documented in Latin America, we find that the model exhibits a backward bifurcation. Specifically, a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. To further explore model predictions, we use numerical simulations to assess the importance of sexual transmission to disease dynamics. This analysis shows that risky behavior involving multiple sexual partners, particularly among male populations, substantially increases the number of infected individuals in the population, contributing significantly to the disease burden in the community. [ABSTRACT FROM AUTHOR]