model proposed in [@BraVdd01] is a two-dimensional, and the Poincaré-Bendixson theorem has been used to study the global stability of the EE. In [@1056.92052], the authors considered model is an $SEIS$ model and a geometric approach [@Limul95; @MR95k:92022] is used to prove the global stability of the EE. Li et *al.* [@guo2012impacts] generalized the before-mentioned models for staged-progression model – by considering a model with $n$ infectious stages and a proportion $p_i$ of the total influx is incorporated for each infectious class $I_i$. The models in the before-mentioned papers are all for directly transmitted diseases.\
Recently, Tumwiine et *al.* [@tumwiine2010host] investigated the effects of infected immigrants using an $SIR-SI$ Ross-Macdonal’s model in the context of malaria and showed that the disease persists in host and vector populations whenever the proportion of infected immigrants is non zero. However, their model does not account of immigration of latent individuals, a critical category as these pass the precautionary measures of screenings, if these were in place.\
In this paper, we derive and investigate the global behavior of a system that captures the dynamics of a class of vector-borne models accounting for flux of infected individuals at different stages of infection. Of particular interest 