Uncertainty and sensitivity analysis of a Rift Valley fever model

Rift Valley fever (RVF) is a vector-borne viral disease with pronounced health and economic impacts on domestic animals and humans in much of sub-Saharan Africa. Using techniques of uncertainty and sensitivity analysis (both local derivatives and sampling-based methods) of a mathematical model for RVF transmission in livestock by two population of mosquitoes (Aedes and Culex). We systematically investigate the relative importance of each model parameter for both disease epidemic and endemic activities. The relationship between vertical transmission and basic reproduction number reveals that during epidemic activities vertical transmission accelerates the course of the outbreak as it increases the size of infected vectors and reduces the duration of the outbreak. However, during endemic activities, vertical transmission exceeding 20% highly influences the basic reproduction number and disease persistence. Results of both local and global sensitivity analysis agrees that R0 is most sensitive to vertical transmission, probability of transmission from Aedes mosquitoes to host, vector initial density and number of bites an Aedes mosquito would want to bite a host and number of bites that a host can sustain. This suggests that reducing vector population and enhancing control intervention in livestock is a viable preventive strategy. Both time varying and time invariant sensitivity analysis of disease prevalence governed by both asymptomatic and symptomatic state variables indicate that the most significant parameters are: number of bites that an Aedes mosquito would want to bite a host, number of bites a host can sustain, probability of transmission from host to an Aedes mosquito and the host death rate. Furthermore, time varying sensitivity analysis provides a comprehensive overview of the effects of each model input parameter at all important stages of the epidemic.