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ABSTRACT With the increasing urban population, the accumulation of household waste (HHW) and its disposal has become an arduous issue. Household wastes spread several kinds of deadly diseases and have aroused attention from all sectors of society. Therefore, in this paper, we have developed a Caputo‐type fractional order SIR model by incorporating two types of bacteria populations, viz., bacteria in the environment () and bacteria in the organism (). In the analysis, the well‐posedness of the model, the existence, and uniqueness of the solution have been shown. We have also found the basic reproduction number and performed its sensitivity analysis. Moreover, we have investigated the stability analysis in the sense of Ulam‐Hyers stability criteria. Since the burden of vector‐borne diseases is very high, therefore, we have also formulated an optimal control problem (OCP) which is helpful in lowering disease burden with optimal cost, with inclusion of three controls and that are basically focused on reducing the transmission rates. Seven different types of optimal control strategies have been performed and compared, along with the study of their respective cost functions. This study offers a realistic, cost‐effective approach to guide decision‐makers in controlling diseases spread by household waste.
Srivastava et al. (Thu,) studied this question.