<![CDATA[The spread of infected diseases are usually caused by direct contact between those considered as susceptible and those already infected. In this study, both the relapse and the latent factors were considered. The relapse factor is associated with a condition where the disease might be occurred again, while the latent related with the condition that the germ were being inactive in the body. We applied this model to study the spread of the disease considering that the members of population in the exposed class were distributed on a manner of negative exponentially distribution or step function. The basic reproduction number was studied and applied to stability. All the models gave results that as the birth rate or remove rate was bigger then the proportion of susceptible population increase, while proportion of infected population and recovers decrease. On the other hand, if the contact rate and recurrence to return increase then the susceptible population decrease, while the proportion of infected population and recovers increase.]]>
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