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The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

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  • Raid Kamel Naji
  • Reem Mudar Hussien

Abstract

An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. Two different types of infectious diseases that spread through both horizontal and vertical transmission in the host population are considered. The basic reproduction number R0 is determined. The local and the global stability of all possible equilibrium points are achieved. The local bifurcation analysis and Hopf bifurcation analysis for the four‐dimensional epidemic model are studied. Numerical simulations are used to confirm our obtained analytical results.

Suggested Citation

  • Raid Kamel Naji & Reem Mudar Hussien, 2016. "The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnljam:v:2016:y:2016:i:1:n:4907964
    DOI: 10.1155/2016/4907964
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    References listed on IDEAS

    as
    1. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, October.
    2. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco‐Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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