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We propose a mathematical model to analyze the effects of anti-infectionbehavior on the equilibrium states of an infectious disease. The anti-infectionbehavior is incorporated into a classical epidemiological SIR model, byconsidering the behavior adoption rate across the population as an additionalvariable. We consider also the effects on the adoption rate produced by thedisease evolution, using a dynamic payoff function and an additionaldifferential equation. The equilibrium states of the proposed model haveremarkable characteristics: possible coexistence of two locally stable endemicequilibria, the coexistence of locally stable endemic and disease-freeequilibria, and even the possibility of a stable continuum of endemicequilibrium points. We show how some of the results obtained may be used tosupport strategic planning leading to effective control of the disease in thelong-term.

Effects of anti-infection behavior on the equilibrium states of an infectious disease