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Mathematical Modeling and Analyzing of Transmission Dynamics of Influenza with Carrier

S. C. Paul, M. A. Haque, M. A. Islam, A. K. Chakraborty

Abstract



Seasonal influenza epidemic is a major public health concern across all over the world that causes millions of respiratory illnesses in each year. Although there are several ways of transmission of influenza among susceptible populations, one of the major causes is of carrier. As a consequence, in this paper, a compartmental mathematical model SEIQCR has been proposed to describe the transmission dynamics of seasonal influenza with carrier. The main goal of this paper is to add a carrier class with the existing model and analyze the dynamics of the influenza epidemic through numerical simulations. The disease transmission has been revealed when the susceptible is exposed by a carrier. The virus free equilibrium and endemic equilibrium points of the model are calculated, and the basic reproduction number is computed using the method of next generation matrix. Local stability of the model for virus free and endemic equilibrium is analyzed. Numerical simulations of the model have been presented to show the dynamical behavior of the compartments for different cases. Finally, the effect of carrier population has been analyzed and revealed that carrier population has a great impact on disease transmission in case of influenza epidemic.

Keywords


Epidemic model, influenza, carrier, differential equation, next generation matrix, stability analysis.

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