Abstract
AbstractThis 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 $\widehat{P}_{r}$Pˆr in the contact-activity time of infected individuals is, the lower the critical vaccination coverage level $p_{c}$pc 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 $\mathcal{I}$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 $\mathcal{I}$I is, the lower the value of the critical reduction in infected individuals’ time activity $P_{r}^{\star}$Pr⋆, at which a Hopf bifurcation is generated, is. Simulations with parameter values corresponding to the case of influenza A have been carried out.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference29 articles.
1. Anderson, R., May, R.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1991)
2. Brauer, F., Castillo-Chavez, C.: Mathematical Models in Population Biology and Epidemiology. Springer, Berlin (2012)
3. Busenberg, S., van den Driessche, P.: Analysis of a disease transmission model in a population with varying size. J. Math. Biol. 28(3), 257–270 (1990)
4. Capasso, V., Serio, G.: A generalization of the Kermack–Mckenderick deterministic epidemic model. Math. Biosci. 42, 43–61 (1978)
5. Diekmann, O., Heesterbeek, J.: Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation. Wiley, Chichester (2000)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献