Abstract
This research try to study how vaccination rate and vaccine efficiency can affect the infection by respiratory system viruses using dynamical system. Depending on epidemiological state of the study community we divided it into four group : S (healthy),V (who get vaccine), I (who get infection) and Q (who attended to health quarantine). By solving all the equations of system we can found that the system has two equilibrium point. On the other hand the system was locally analyzed. And the numerical analysis of the system showed that rapid increase in infection rate when we have low vaccination rate and decrease in infection rate when increase vaccination rate and also explain how vaccine efficiency effect on development and spreading of disease.
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