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Antimicrobial resistance (AMR) is the microorganism's resistance to an antimicrobial drug developed and designed to handle an infection. A recent study showed that there were 1.27 million global deaths in 2019 attributable to AMR. In current decades, vaccination is the most effective treatment that can reduce the growing AMR by preventing the incidence of infectious diseases (directly or indirectly). Vaccination has become a popular treatment as this can reduce the number of circulating AMR strains and reduce the need for antimicrobial use. With a double-dose vaccination campaign, we analyzed drug-susceptible and drug-resistant pathogens for this survey. We considered the circumstances of positive invariances and boundedness with appropriate primary conditions. We have determined two basic reproduction numbers: one associated with drug-susceptible strain (R01) and the other with drug-resistant strain (R02). We also revealed that at any stage, one of the strain could spread in a population if max[R01, R02] > 1 and the disease fade-out if both are

COVID-19 is an infectious disease that kills millions of people each year and it is a major public health problem around the globe. The current COVID-19 situation is still now concerning, though the vaccination program is running. In this study, we considered a COVID-19 model with a double-dose vaccination strategy to control the current outbreak situation in Bangladesh. The fundamental qualitative analysis of this mathematical model has been performed. The conditions of positive invariance, boundedness with suitable initial conditions were analyzed. We have estimated the basic reproduction number (R0) for disease transmission and determined that our model contains two equilibrium points: the disease-free equilibrium and a disease-endemic equilibrium. We used the Routh-Hurwitz criteria to determine the stability of the equilibria. The disease will be eradicated from the community if R0