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Stability analysis on an economic epidemiological model with vaccination

1. Department of Statistical and Actuarial Sciences, University of Western Ontario, London, N6A 5B7, Canada
2. Department of Mathematics, Trent University, Peterborough, K9L 0G2, Canada

In this paper, an economic epidemiological model with vaccination is studied. The stability of the endemic steady-state is analyzed and some bifurcation properties of the system are investigated. It is established that the system exhibits saddle-point and period-doubling bifurcations when adult susceptible individuals are vaccinated. Furthermore, it is shown that susceptible individuals also have the tendency of opting for more number of contacts even if the vaccine is inefficacious and thus causes the disease endemic to increase in the long run. Results from sensitivity analysis with specific disease parameters are also presented. Finally, it is shown that the qualitative behaviour of the system is affected by contact levels.

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Keywords Dynamical system; economic epidemiology; equilibrium; eigenvalue; stability; vaccination

Citation: Wisdom S. Avusuglo, Kenzu Abdella, Wenying Feng. Stability analysis on an economic epidemiological model with vaccination. Mathematical Biosciences and Engineering, 2017, 14(4): 975-999. doi: 10.3934/mbe.2017051

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