Fig. 1

The seven Compartments are Susceptible (\(\:S\)), Exposed (\(\:E\)), Vaccinated (\(\:V\)), Detected Individuals (I^d), Non-detected Individuals (I^nd), Treatment (T), and Recovered (R). Without the vaccine, susceptible individuals may become exposed. After some duration of 1/α, exposed individuals turn infected. Who tests they go to the detected individuals at a p testing rate. Those who do not test also go to non-detected individuals at a 1-p rate. The detected individuals are taking treatment at τ rate. They are also recovering naturally at γ rate. After taking treatment, they are getting recover at δ rate. Non-detected individuals are also recovering naturally at γ rate.