MATHEMATICAL MODELLING OF CHIKUNGUNYA DISEASE DYNAMICS

Abstract

In this thesis, we have adapted and modified the existing SEIR-SI Mathematical model by adjusting the vertical transmission in humans, where infected mothers pass the disease to newborns, and introducing insecticide spraying targeting the mosquito population to describe the transmission dynamics of Chikungunya disease. Mathematical analysis of the model yields the basic reproduction number, a key biological threshold parameter that determines disease persistence or elimination was calculated using the next-generation matrix method. The local stability of the disease free equilibrium and the endemic equilibrium was discussed using the Routh-Hurwitze criterion. Also, the global stability of both the disease free and the endemic equilibrium were performed using Lasselle’s invariance principle of Lyapunov functions. The results show that; if , then the disease free equilibrium is globally asymptotically stable, which leads to eradication of the disease and the current intervention (spraying) is effective. Conversely, if , then the endemic equilibrium becomes globally stable, which indicate that the persistence of the disease within the community and stronger intervention are required to bring below one. Sensitivity analysis highlights that the spraying insecticide rate has a significant negative impact on reproduction number, suggest that intensify vector control measures can effectively reduce disease transmission. Meanwhile, the vertical transmission rate has a moderate effect on increasing transmission. Numerical simulation was conducted using MATLAB software to confirm our analytic result