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Susceptible-Infected-Recovered (SIR) models have been used for decades tounderstand epidemic outbreak dynamics. We develop an SIR model specificallydesigned to study the effects of population behavior with respect to health andvaccination protocols in a generic epidemic. Through a collection ofparameters, our model includes the traditional SIR components: populationbirth, death, infection, recovery and vaccination rates, as well as limitedimmunity.  We first use this simple setup to compare the effects of two vaccinationschemes, one in which people are vaccinated at a rate proportional with thepopulation, and one in which vaccines are administered to a fraction of thesusceptible people (both of which are know strategies in real life epidemics).We then expand on the model and the analysis by investigating how these twovaccination schemes hold under two scenarios of population behavior: one inwhich people abide by health protocols and work towards diminishingtransmission when infection is high; one in which people relax health protocolswhen infection is high.  We illustrate these two aspects (vaccination and adherence to healthprotocols) act together to control the epidemic outbreak. While it is idealthat the tow components act jointly, we also show that tight observance ofhealth protocols may diminish the need for vaccination in the effort to clearor mitigate the outbreak. Conversely, an efficient vaccination strategy cancompensate for some degree of laxity in people's behavior.

Modeling the effects of adherence to vaccination and health protocols in epidemic dynamics by means of an SIR model