About: In this paper, we study the dynamics of an infectious disease in the presence of a continuous-imperfect vaccine and latent period. We consider a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population. After we propose the model, we provide the well-posedness property and calculate the effective reproduction number [Formula: see text] . Then, we obtain the threshold dynamics of the system with respect to [Formula: see text] by studying the global stability of the disease-free equilibrium when [Formula: see text] and the system persistence when [Formula: see text] . For the endemic equilibrium, we use the semi-discretization method to analyze its linear stability. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to implement a case study regarding data of influenza patients, study the local and global sensitivity of [Formula: see text] , construct approximate stability charts for the endemic equilibrium over different parameter spaces and explore the sensitivity of the proposed model solutions.   Goto Sponge  NotDistinct  Permalink

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  • In this paper, we study the dynamics of an infectious disease in the presence of a continuous-imperfect vaccine and latent period. We consider a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population. After we propose the model, we provide the well-posedness property and calculate the effective reproduction number [Formula: see text] . Then, we obtain the threshold dynamics of the system with respect to [Formula: see text] by studying the global stability of the disease-free equilibrium when [Formula: see text] and the system persistence when [Formula: see text] . For the endemic equilibrium, we use the semi-discretization method to analyze its linear stability. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to implement a case study regarding data of influenza patients, study the local and global sensitivity of [Formula: see text] , construct approximate stability charts for the endemic equilibrium over different parameter spaces and explore the sensitivity of the proposed model solutions.
Subject
  • Virology
  • Hygiene
  • Therapy
  • Epidemiology
  • Numerical analysis
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