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

Shi Zhao,Jing Qin,Daihai He,Jiayi Meng,Salihu S Musa,Peihua Cao,Jay T Hebert,Jinjun Ran

doi:10.7717/peerj.8601

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, (n}{}{mathcal{R}}_{mathrm{eff}}), strictly less than 1. We established a vector-host compartmental model, and derived (n}{}{mathcal{R}}_{mathrm{eff}}) for vector-borne diseases. The analytic form of the (n}{}{mathcal{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 (n}{}{mathcal{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.

Highlights

Vector-borne disease epidemics pose a serious threat to global health
We formulated the analytic form of the effective reproduction number, Reff, with respect to the basic reproduction number, R0, and the susceptibilities of the vector (Sv) and host (Sh) for vector-borne diseases in Eq (5)
The R0Sh was calculated lower than 1 since the mid-February 2016, and this contradicted with the occurrence of the second yellow fever (YF) epidemic wave in May

Summary

Introduction

Vector-borne disease epidemics pose a serious threat to global health. During 2014, the historical large-scale dengue fever caused an extensive international epidemic in southern China as well as. Modelling the effective reproduction number of vector-borne diseases: the yellow fever outbreak in Luanda, Angola 2015–2016 as an example. In 2015–2016, the largest yellow fever (YF) outbreak (since the 1980s) occurred in Angola and the Democratic Republic of the Congo (DRC) (Zhao et al, 2018b; Kraemer et al, 2017; Wu et al, 2016; Shearer et al, 2017). Malaria epidemics occur from time to time in many under-developed places in the tropical and sub-tropical regions (Caminade et al, 2014; Murray et al, 2012). The increasing frequency of such outbreaks over the past decades urges disease control and prevention studies (Johansson et al, 2012; Kraemer et al, 2019)

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