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Background: Standard epidemiological theory claims that in structured populations competition between multiple pathogen strains is a deterministic process which is mediated by the basic reproduction number (R0) of the individual strains.
The global dynamics of our model is determined by the basic reproduction number (Re_{0}).
It is shown that the global transmission dynamics of the disease is fully determined by the basic reproduction number.
In the presence of spatial diffusion, we show that the local stability and the global stability are completely determined by the basic reproduction ratio (R_{0}).
Under ((A_{1}))-((A_{4})), the global stability and instability of the equilibria are completely determined by the basic reproduction numbers (R_{0}) and (R_{1}).
The global dynamics is completely described by the basic reproduction number ({mathcal{R}}_{0}). Denphedtnong et al. [9] proposed a SEIRS mathematical model with transport related infection.
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By calculations, the basic reproduction number has been established.
We establish the global dynamics of the disease-free state by using the basic reproduction number and present one of our main results (Theorem 3.2) in Section 3.
The transmission probability per contact is then given by dividing the basic reproduction number R 0 (chosen to be 1.575 for the baseline parameter setting) by the largest eigenvalue [ 30] (see Appendix 3 for details).
By calculating, we obtain the basic reproduction number (R_{0}).
By calculating we have the basic reproduction number (mathcal{R}_{0}=1.1868>1).
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