Modelling the effective reproduction number of vector-borne diseases: the yellow fever outbreak in Luanda, Angola 2015-2016 as an example

Abstract

The burden of vector-borne diseases (Dengue, Zika virus, yellow fever, etc.) gradually increased in the past decade across the globe. Mathematical modelling on infectious diseases helps to study the transmission dynamics of the pathogens. Theoretically, the diseases can be controlled and eventually eradicated by maintaining the effective reproduction number, ( $R_{\mathrm{eff}}$ ), strictly less than 1. We established a vector-host compartmental model, and derived ( $R_{\mathrm{eff}}$ ) for vector-borne diseases. The analytic form of the ( $R_{\mathrm{eff}}$ ) was found to be the product of the basic reproduction number and the geometric average of the susceptibilities of the host and vector populations. The ( $R_{\mathrm{eff}}$ ) formula was demonstrated to be consistent with the estimates of the 2015-2016 yellow fever outbreak in Luanda, and distinguished the second minor epidemic wave. For those using the compartmental model to study the vector-borne infectious disease epidemics, we further remark that it is important to be aware of whether one or two generations is considered for the transition "from host to vector to host" in reproduction number calculation.

Keywords: Angola; Epidemic; Luanda; Mathematical modelling; Reproduction number; Vector-borne disease; Yellow fever.