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.
Similar content being viewed by others
References
WHO Factsheet 38, 2014.
E.A. Gould, S. Higgs, Trans. R. Soc. Trop. Med. Hyg. 103, 109 (2009)
P.W. Gething et al., Nature 465, 342 (2010)
T.M. Sharp, K.M. Tomashek, Curr. Epi. Rep. 4, 11 (2017)
ECDPC, Development of Aedes albopictus risk maps, 2009
J.E. Brown, E.J. Scholte, M. Dik, H.W. Den, J. Beeuwkes, J.R. Powell, Emerg. Infect Dis. 17, 2335 (2011)
R. Romi, F. Severini, L. Toma, J. Am. Mosq. Control Assoc. 22, 149 (2006)
A. Wilder-Smith et al., Euro Surveill. 19, 20718 (2014)
T. Demir, S. Kilic, Folia Microbiol. 61, 523 (2016)
H. Sakkas, V. Economou, C. Papadopoulou, J. Vector Borne Dis. 53, 305 (2016)
World Health Organization, Zika virus, microcephaly and Guillain-Barré syndrome situation report, 2016.
F. Grischott, M. Puhan, C. Hatz, P. Schlagenhauf, Travel Med. Infect Dis. 14, 313 (2016)
R.M. Anderson, R.L. May,Infectious Diseases of Humans: Dynamics and Control (Oxford University Press, Oxford, 1991)
J.M. Keeling, P. Rohani,Modeling Infectious Diseases in Humans and Animals (Princeton University Press, Princeton, 2007)
N.A. Bacaër,A Short History of Mathematical Population Dynamics (Springer, London, 2011)
R. Ross,The prevention of Malaria (John Murray, London, 1911)
G. Macdonald,The Epidemiology and Control of Malaria (Oxford University Press, Oxford, 1957)
K. Magori, J.M. Drake, Nat. Ed. Knowledge 4, 14 (2013)
D.L. Smith et al., PLOS Pathogens 8, 1 (2012)
S. Ruan, D. Xiao, J.C. Beier, Bull. Math. Biol. 70, 1098 (2008)
S.M. O’Regan, J.W. Lillie, J.M. Drake, Theor. Ecol. 9, 269 (2016)
R.C. Reiner et al., J. Roy. Soc. Interface 10, 20120921 (2013)
M.E.J. Newman, SIAM Rev. 45, 167 (2001)
S. Boccaletti et al., Phys. Rep. 424, 175 (2006)
S. Gómez et al., Europhys. Lett. 89, 38009 (2010)
B. Guerra, J. Gómez-Gardeñes, Phys. Rev. E 82, 035101 (2010)
S. Gómez, J. Gómez-Gardeñes, Y. Moreno, A. Arenas, Phys. Rev. E 84, 036105 (2011)
R. Pastor-Satorras, C. Castellano, P. Van Mieghem, A. Vespignani, Rev. Mod. Phys. 87, 925 (2015)
A.L. Barabási, R. Albert, Science 286, 509 (1999)
M.E.J. Newman,Networks: An Introduction (Oxford University Press, Oxford, 2010)
E. Cho, S.A. Myers, J. Leskovec, inProceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining (ACM, 2011), pp. 1082–1090
A. Allard, B.M. Althouse, S.V. Scarpino, L. Hébert-Dufresne, PNAS 114, 8969 (2017)
A. Allard, B.M. Althouse, L. Hébert-Dufresne, S.V. Scarpino, PLOS Pathogens 13, e1006633 (2017)
B. Visseaux et al., Lancet Infect Dis. 16, 1000 (2016)
E. Nicastri et al., Eurosurveillance 21, 32 (2016)
A.J. Kucharski et al., PLoS Negl. Trop. Dis. 10, e0004726 (2016)
D. Gao et al., Sci. Rep. 6, 28070 (2016)
J. Gómez-Gardeñes, D. Soriano-Paños, A. Arenas, Nat. Phys. 14, 391 (2018)
V. Colizza, R. Pastor-Satorras, A. Vespignani, Nat. Phys. 3, 276 (2007)
V. Belik, T. Geisel, D. Brockmann, Phys. Rev. X 1, 011001 (2011)
J.T. Matamalas, M. De Domenico, A. Arenas, J. R. Soc. Interface 13, 20160203 (2016)
S. Polwiang, Peer J. 3, e1069 (2015)
J. Rocklöv et al., EBioMedicine 9, 250 (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Soriano-Paños, D., Arias-Castro, H., Naranjo-Mayorga, F. et al. Impact of human-human contagions in the spread of vector-borne diseases. Eur. Phys. J. Spec. Top. 227, 661–672 (2018). https://doi.org/10.1140/epjst/e2018-00099-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2018-00099-3