Impact of reduction in contact time activity of infected individuals on the dynamics and control of directly transmitted respiratory infections in SIR models

Abstract

Abstract This paper aims to study the impact of using an educational strategy on reducing the efforts needed to control respiratory transmitted infections represented by SIR models, taking into account heterogeneity in contacts between infected and non-infected individuals. Therefore, a new incidence function, in which the difference in contact time activity between infected and non-infected individuals is taken into account, is formulated. Equilibrium and stability analyses of the model have been carried out. The model has been extended to include the effect of herd immunity and the analysis showed that the higher the percent reduction P ˆ r $\widehat{P}_{r}$ in the contact-activity time of infected individuals is, the lower the critical vaccination coverage level p c $p_{c}$ required to eliminate the infection is, and therefore, the lower the infection’s minimum elimination effort is. Another extension of the basic model to include a control strategy based on treating infected individuals at rate α with a maximum capacity treatment I $\mathcal{I}$ has been considered. The equilibrium analysis showed the existence of multiple subcritical and supercritical endemic equilibria, while the stability analysis showed that the model exhibits a Hopf bifurcation. Simulations showed that the higher the maximum treatment capacity I $\mathcal{I}$ is, the lower the value of the critical reduction in infected individuals’ time activity P r ⋆ $P_{r}^{\star}$ , at which a Hopf bifurcation is generated, is. Simulations with parameter values corresponding to the case of influenza A have been carried out.

Keywords

• Herd immunity
• Equilibria
• Stability analysis
• Maximum treatment capacity
• Hopf bifurcation