Transmission Dynamics of a Two-City SIR Epidemic Model with Transport-Related Infections

Abstract

A two-city SIR epidemic model with transport-related infections is proposed. Some good analytical results are given for this model. If the basic reproduction number<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mi>γ</mml:mi></mml:mrow></mml:msub><mml:mo>≤</mml:mo><mml:mn>1</mml:mn></mml:math>, there exists a disease-free equilibrium which is globally asymptotically stable. There exists an endemic equilibrium which is locally asymptotically stable if the basic reproduction number<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mi>γ</mml:mi></mml:mrow></mml:msub><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:math>. We also show the permanence of this SIR model. In addition, sufficient conditions are established for global asymptotic stability of the endemic equilibrium.