Eur. Phys. J. Special Topics 227, 661–672 (2018)
https://doi.org/10.1140/epjst/e2018-00099-3

Regular Article

Impact of human-human contagions in the spread of vector-borne diseases

¹ Departamento de Física de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain
² GOTHAM lab, Instituto de Biocomputación y Física de Sistemas Complejos BIFI, Universidad de Zaragoza, 50018 Zaragoza, Spain
³ Departamento de Matemáticas, Universidad del Valle, 25360 Santiago de Cali, Colombia
⁴ Departamento de Física, Universidad Pedagógica y Tecnológica de Colombia, 150003 Tunja, Colombia

^a e-mail: gardenes@gmail.com

Received: 20 October 2017
Received in final form: 26 March 2018
Published online: 4 October 2018

Abstract

This article is aimed at proposing a generalization of the Ross-Macdonald model for the transmission of Vector-borne diseases in which human-to-human contagions are also considered. We first present this generalized model by formulating a mean field theory, checking its validity by comparing to numerical simulations. To make the premises of our model more realistic, we adapt the mean field equations to the case in which human contacts are described by a complex network. In this case we are also able to derive an analytical expression for the epidemic threshold. In both the mean-field and network-based models, we estimate the value of the epidemic threshold which corresponds to the boundary between the disease-free and epidemic regimes. The expression of this threshold allows us to discuss the impact that human-to-human contagions have on the spread of vector-borne diseases.