Mathematical modelling of transmission dynamics of Dengue Fever in the presence of infective immigrants

Dengue fever is one of the neglected tropical diseases around the globe and its ravaging effect over the period has been enormous in the affected areas. Globalisation, immigration and urbanization and poor urban planning have become the contributory factors in the spread of infectious diseases. In this paper, a model describing the dynamics of dengue fever incorporated with infection immigrants is formulated and analysed using ordinary differential equations with a constant immigration recruitment rate. The model was qualitatively and quantitatively analysed for its local stability, basic reproductive number and sensitivity of the model parameters values to the basic reproductive number to understand the impact of the parameters on the disease spread. In the analysis, it was found that in the presence of infectious immigrants, there cannot be a disease free state demonstrated by ∅ ≥ 0 where the model demonstrates a unique endemic equilibrium state if the fraction of infectious immigrants ∅ is positive. The unique endemic equilibrium for which there is a fraction of infectious immigrants is globally asymptotically stable. Numerical simulation was performed and the results displayed graphically and discussed. It was revealed that immigration of infected immigrants contributes significantly in the spread of dengue fever and that it can be controlled by preventing the influx of infected immigrants and reducing the mosquitoes and human contact rate.