Sylvatic Dengue and Animal-to-Human Spillover

Sylvatic Dengue and Animal-to-Human Spillover SSSMB São Paulo SP 22 de January de 2012 BRAGA, Mariana Pires CARA, Elisa Regina CESAR, Jonatas DA SILVA, Gustavo Luís SANTOS, Lindomar Soares YAMASHITA, Márcio Katsumi Institute for Theoretical Physics (IFT Unesp) SSSMB Unesp 1 / 25

Script 1 Background 2 Question 3 Methodology 4 Results 5 References (IFT Unesp) SSSMB Unesp 2 / 25

Background Background Four Dengue virus (DENV) serotypes; Two ecologically and evolutionary distinct transmission cycles: sylvatic (non-human primates) and human cycles; Potential shift from animal reservoir into humans. (IFT Unesp) SSSMB Unesp 3 / 25

Main Question. Question How can we characterize the spillover from Sylvatic dengue transmission cycle to Human cycle? (IFT Unesp) SSSMB Unesp 4 / 25

Sketch Question Figure: Modified from [Vasilakis et al., 2011] (IFT Unesp) SSSMB Unesp 5 / 25

Question Sketch Figure: Schematic diagram of zoonotic transmission dynamics. Modified from [Lloyd-Smith et al., 2009]. (IFT Unesp) SSSMB Unesp 6 / 25

Sketch Question Figure: Phylogenetic history of human and sylvatic dengue. (IFT Unesp) SSSMB Unesp 7 / 25

Methodology Methodology Dynamic compartmental modeling Classifies the population into compartments; Uses a differential equation system to describe transitions between compartments. (IFT Unesp) SSSMB Unesp 8 / 25

Methodology Methodology Figure: Compartmental Dynamic Model diagram from [Pinho et al., 2010]. (IFT Unesp) SSSMB Unesp 9 / 25

Methodology Methodology Figure: Compartmental Dynamic Model diagram. (IFT Unesp) SSSMB Unesp 10 / 25

Methodology Parameters Parameter Biological meaning Value µ m average mosquito mortality rate 0.06 c competition parameter 1 β ms effective cont. rates (mosquito sylvatic virus) 0.4 β mh effective cont. rates (mosquito human virus) 0.4 β hs effective cont. rates (human human sylvatic virus) 0.5 β hh effective cont. rates (human human virus) 0.5 µ h human mortality rate 4x10 4 α rs recovering rate (sylvatic virus) 0.16 α rh recovering rate (human virus) 0.16 γ v vaccination against human virus 1.7x10 4 Table: Data from [IBGE, 2012, wikipédia, 2012, Pinho et al., 2010] (IFT Unesp) SSSMB Unesp 11 / 25

Model Methodology d dt M M S = µ m M β S H Is Ms H d dt M M Is = β S H Is Ms H µ M mm Is cβ Is H Ih Mh H d dt M M Ih = β S H Ih M Mh µ m M H Ih + cβ Is H Ih Mh H d dt H M S = µ h H S + µ h H β Is H S Hs H β Hh d dt H M Is = β Is H S Hs H α RsH Is µ h H Is d dt H M Ih = β Ih H S Hh α H Rh H Ih µ h H Ih d dt H R = α Rs H Is + α Rh H Is µ h H R β M S H Ih Mh µ m M H S M Ih H S H (IFT Unesp) SSSMB Unesp 12 / 25

Results Point 1, Stable M s = M M is = 0 M ih = 0 H s = H H ih = 0 H is = 0 H r = 0 (IFT Unesp) SSSMB Unesp 13 / 25

Results Point 2, Stable if M H > (α r+µ h )µ m β ms β hs M s = (α r + µ h ) (Mβ hs + Hµ h ) µ m β hs (β ms µ h + (α r + µ h ) µ m ) M is = µ h (Mβ hs β ms H (α r + µ h ) µ m ) β hs (β ms µ h + (α r + µ h ) µ m ) M ih = 0 H s = H2 (β ms µ h + (α r + µ h ) µ m ) β ms (Mβ hs + Hµ h ) H ih = 0 H is = Hµ h (Mβ hs β ms H (α r + µ h ) µ m ) β ms (α r + µ h ) (Mβ hs + Hµ h ) H r = Hα r (Mβ hs β ms H (α r + µ h ) µ m ) β ms (α r + µ h ) (Mβ hs + Hµ h ) (IFT Unesp) SSSMB Unesp 14 / 25

Results Point 3, Stable if M H > (α r+µ h )µ m β mh β hh M s = (α r + µ h ) (Mβ hh + Hµ h ) µ m β hh (β mh µ h + (α r + µ h ) µ m ) M is = 0 M ih = µ h (Mβ hh β mh H (α r + µ h ) µ m ) β hh (β mh µ h + (α r + µ h ) µ m ) H s = H2 (β mh µ h + (α r + µ h ) µ m ) β mh (Mβ hh + Hµ h ) H ih = Hµ h (Mβ hh β mh H (α r + µ h ) µ m ) β mh (α r + µ h ) (Mβ hh + Hµ h ) H is = 0 H r = Hα r (Mβ hh β mh H (α r + µ h ) µ m ) β mh (α r + µ h ) (Mβ hh + Hµ h ) (IFT Unesp) SSSMB Unesp 15 / 25

Point 4, Unstable Results M s = Mβ hhβ mh β hs β ms ( Mβ 2hhβ mh + Mβ hh β hs β ms + Hβ hs β msµ h ) µ m Mβhhβ 2 mhµ 2 h (α r + µ h ) M is = β hs β ms ( β hh β mh µ h + ( β hh + β hs ) (α r + µ h ) µ m) M ih = Mβ hhβ mh β msµ h (α r + µ h ) ( Mβ hh β mh + β ms (Mβ hs + Hµ h )) µ m β ms (β hh β mh µ h + (β hh β hs ) (α r + µ h ) µ m) H s = H2 β ms ( β hh β mh µ h (β hh β hs ) (α r + µ h ) µ m) β hh β mh (Mβ hh (β mh β ms) Hβ msµ h ) H ih = H ( Mβ hhβ mh β msµ h + (α r + µ h ) ( Mβ hh β mh + β ms (Mβ hs + Hµ h )) µ m) β mh (α r + µ h ) (Mβ hh (β mh β ms) Hβ msµ h ) HMβhhβ 2 mhµ 2 h H (α r + µ h ) ( Mβ 2hhβ ) mh + Mβ hh β hs β ms + Hβ hs β msµ h µ m H is = β hh β mh (α r + µ h ) (Mβ hh (β mh β ms) Hβ msµ h ) ( ) Hα r Mβhhβ 2 mh (β mh β ms) + H (β hh β hs ) β ms (α r + µ h ) µ m H r = β hh β mh (α r + µ h ) (Mβ hh (β mh β ms) Hβ msµ h ) (IFT Unesp) SSSMB Unesp 16 / 25

Results Value of R 0s R 0s = β ms β hs (cβ mh H ih + µ m H)(α rs + µ h ) M s H s H (IFT Unesp) SSSMB Unesp 17 / 25

Results Results Figure: Disease free state. H is = 0.001, H ih = 0.01 and M H = 0.05. (IFT Unesp) SSSMB Unesp 18 / 25

Results Results Figure: Human virus endemy. H is = 0.001, H ih = 0.01 and M H = 0.2. (IFT Unesp) SSSMB Unesp 19 / 25

Results Results Figure: Initial sylvatic epidemy attenuated by Human virus. H is = 0.02, H ih = 0.01 and M H = 0.1. (IFT Unesp) SSSMB Unesp 20 / 25

Results Vaccination Compartment H v = γ v H s µ hv β Hs H v M s (IFT Unesp) SSSMB Unesp 21 / 25

Results Results Figure: Sylvatic virus endemy due to vaccination. H is = 0.016, H ih = 0.01, M H = 0.1 and γ v = 30%. (IFT Unesp) SSSMB Unesp 22 / 25

Results Results Figure: H is = 0.01, H ih = 0.01,β ms >> β mh and β hs >> β hh. (IFT Unesp) SSSMB Unesp 23 / 25

Bibliography References IBGE (2012). http://www.ibge.gov.br/estadosat/perfil.php?sigla=rj access: 21 january 2012. Lloyd-Smith, J., George, D., Pepin, K., Pitzer, V., Pulliam, J., Dobson, A., Hudson, P., and Grenfell, B. (2009). Epidemic dynamics at the human-animal interface. Science, 326(5958):1362. Pinho, S., Ferreira, C., Esteva, L., Barreto, F., Morato e Silva, V., and Teixeira, M. (2010). Modelling the dynamics of dengue real epidemics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368(1933):5679 5693. Vasilakis, N., Cardosa, J., Hanley, K., Holmes, E., and Weaver, S. (2011). Fever from the forest: prospects for the continued emergence of sylvatic dengue virus and its impact on public health. Nature Reviews Microbiology, 9(7):532 541. wikipédia (2012). http://pt.wikipedia.org/wiki/dengue access: 21 january 2012. (IFT Unesp) SSSMB Unesp 24 / 25

Thank You! (IFT Unesp) SSSMB Unesp 25 / 25