Mathematical modelling of the effects of seasonality in the transmission dynamics of rift valley fever (RVF)

Rift Valley Fever (RVF) is a mosquito-borne viral disease affecting livestock and humans. The principal vectors for the disease transmission are Aedes and Culex mosquitoes after seasons of heavy rainfall like El Nino. My study extends the work of Gaff et al., (2007) by incorporating the periodicity aspect in the mosquito-livestock transmission rates. My study carries out simulations using secondary data from different literatures to compare the results of the RVF basic model and the RVF model with the effects of seasonal transmission rates due to rainfall changes. The model results show that infected mosquito populations are increasing sharply in the model with the effects of seasonal transmission rates than in the RVF basic model. Stability of the existence of the endemic equilibrium point of the RVF model with the respect to periodicity aspect in their transmission rates was also carried out through simulations and found locally asymptotically stable for all choices of the initial starting points. However, variations of the periodic transmission rates were also studied to show seasonal effects in the RVF dynamics. Results showed that the periodic contact rates depend on the initial transmission rates for (Aedes, Culex, livestock populations). Despite the fact that the dynamics of the RVF depends on gradual changes of rainfall above average, the spread of the disease strongly depends on the initial transmission rates at the beginning of the epidemic.