Analysis of a SIRI Epidemic Model with Modified Nonlinear Incidence Rate and Latent Period

摘要

Objective: This study proposed an SIRI epidemic model with modified nonlinear incidence rate and latent period. Methodology: The equilibrium point of the model was investigated and showed that it was globally stable without latent period, further this study proposed the stability and Hopf bifurcation for the model with the latent period. Results: This study showed that the infected population on sociological and psychological effects seemed to be similar and the numerical examples were also given to illustrate the theoretical results. Conclusion: If basic reproduction number is less than or equal to one, the disease free equilibrium is globally asymptotically stable and if basic reproduction number is greater than one, then the endemic equilibrium exist and globally without latent period.