Abstract
Rapidly spreading disease, COVID-19 is classified as the human-to-human transmissionable disease and currently it becomes a pandemic in the Globe. In this paper, we propose the conceptual mathematical model and analyze a Susceptible-Exposed-Infected-Quarantined or Isolated-Recovered- Susceptible (SEIRUS) type infectious disease model with imprecise parameters. We have divided the model formulation portion into four subsections. They are namely crisp SEIRUS model, interval SEIRUS model and fuzzy SEIRUS model. The existence condition and boundedness of the solution to our proposed model have been discussed. The asymptotical stability of the system at different equilibrium point is investigated. Also we have explained the global stability at endemic equilibrium point. Application of optimal control of the system is described and solved. Finally, some numerical results have been shown to test the theoretical study of the model. We observed that the population is greatly influenced for the imprecise nature of parameters.
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