Modelling the impact of infected immigrants on vector-borne diseases with direct transmission

A deterministic mathematical model is proposed to study the impact of infected immigrants on vector-borne diseases dynamics with direct transmission. The model involves human host and vector sub-models. The aspect of infected immigrants was assigned to some parameters to assess its impact on the transmission dynamics of vector- borne diseases. The model was analyzed qualitatively to determine the basic reproduction number (Ro) necessary for the control of diseases in communities. Equilibrium points were determined. Disease free equilibrium point was found to be locally asymptotically stable when Ro<1 . We used the Centre Manifold theory to analyze the existence and the stability of endemic equilibrium point Ro> 1. We gave a simple criterion for forward bifurcation when Ro crosses one. Numerical simulation shows the increase of incoming infected immigrants in the population increases the rate of infections (endemicity state) among human hosts. Our result shows that, allowing the infected immigrants into the population is the source of persistence of vector-borne diseases in the communities. Therefore in order to eradicate the diseases we should improve our immigrants' policies before entering in hosts population. Effective programs like vaccinations, screening, quarantines, and educate community on how to remove vector breeding sites so as to reduce number of vectors within hosts population.