# Administration of Defective Virus Inhibits Dengue Transmission into Mosquitoes

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## Abstract

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## 1. Introduction

^{®}) for dengue virus are in development and clinical trial. Most of them use live attenuated virus [18], inactivated virus [19], recombinant subunit vaccines [20], delivery vectors [21] or DNA plasmids [22] but none of them deploy defective interfering (DI) particles and their transmission between the host and the vector. Thus, an efficient vaccination strategy should be co-evolving and persist over multiple passages and through the host-vector transmission shuttle.

## 2. Methods

#### 2.1. Within-Host Dengue Viraemia

#### 2.2. Dengue Transmission in Mosquitoes

#### 2.3. Population of Models

Algorithm 1 Construction of experimentally calibrated transmission POMs |

1: $\mathit{Nsample}\leftarrow \mathrm{number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{samples}$ |

2: $\mathit{Npat}\leftarrow \mathrm{number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{within}-\mathrm{host}\phantom{\rule{4.pt}{0ex}}\mathrm{models}\phantom{\rule{4.pt}{0ex}}\mathrm{in}\phantom{\rule{4.pt}{0ex}}\mathrm{the}\phantom{\rule{4.pt}{0ex}}\mathrm{population}$ |

3: $\mathit{Nparam}\leftarrow \mathrm{number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{model}\phantom{\rule{4.pt}{0ex}}\mathrm{parameters}$ |

Require: $\mathit{mossydata}\leftarrow $Read human-to-mosquito transmission data files |

4: $\mathit{figure}\leftarrow $Draw $\mathit{mossydata}$ outputs |

5: for $i\leftarrow 1,Npat$ do |

Require: $\mathit{hostmodel}\leftarrow $Read within-host model data files |

6: $t,V,D\leftarrow \mathrm{viraemia}\phantom{\rule{4.pt}{0ex}}\mathrm{dynamics}$ |

7: $\mathit{param}\leftarrow $ Perform LHS and build ($\mathit{Nsample}\times \mathit{Nparam}$)-dimensional parameter hyperspace |

8: for $j\leftarrow 1,Nsample$ do |

9: $\mathit{mossymodel}\left(j\right)\leftarrow $Solve the model for $param\left(j\right)$ |

10: if $\mathit{mossymodel}\left(j\right)\le $ range of $\mathit{mossydata}\left(j\right)$ then |

11: Accept $param\left(j\right)$ into POMs |

12: $\mathit{figure}\leftarrow $Draw $\mathit{mossymodel}\left(j\right)$ outputs |

13:
goto 8 |

14: goto5 |

15: close; |

#### 2.4. Optimal Bang-Bang Control

#### 2.5. Jensen-Shannon Divergence

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bhatt, S.; Gething, P.W.; Brady, O.J.; Messina, J.P.; Farlow, A.W.; Moyes, C.L.; Drake, J.M.; Brownstein, J.S.; Hoen, A.G.; Sankoh, O.; et al. The global distribution and burden of dengue. Nature
**2013**, 496, 504. [Google Scholar] [CrossRef] [PubMed] - Brady, O.J.; Gething, P.W.; Bhatt, S.; Messina, J.P.; Brownstein, J.S.; Hoen, A.G.; Moyes, C.L.; Farlow, A.W.; Scott, T.W.; Hay, S.I. Refining the global spatial limits of dengue virus transmission by evidence-based consensus. PLoS Negl. Trop. Dis.
**2012**, 6, e1760. [Google Scholar] [CrossRef] [PubMed] - Blair, C.D.; Adelman, Z.N.; Olson, K.E. Molecular strategies for interrupting arthropod-borne virus transmission by mosquitoes. Clin. Microbiol. Rev.
**2000**, 13, 651–661. [Google Scholar] [CrossRef] [PubMed] - Halstead, S.B. Mosquito-borne haemorrhagic fevers of South and South-East Asia. Bull. World Health Org.
**1966**, 35, 3. [Google Scholar] [PubMed] - Hardy, J.L.; Houk, E.J.; Kramer, L.D.; Reeves, W.C. Intrinsic factors affecting vector competence of mosquitoes for arboviruses. Ann. Rev. Entomol.
**1983**, 28, 229–262. [Google Scholar] [CrossRef] [PubMed] - Franz, A.; Kantor, A.; Passarelli, A.; Clem, R. Tissue barriers to arbovirus infection in mosquitoes. Viruses
**2015**, 7, 3741–3767. [Google Scholar] [CrossRef] [PubMed] - Serrato-Salas, J.; Hernández-Martínez, S.; Martínez-Barnetche, J.; Condé, R.; Alvarado-Delgado, A.; Zumaya-Estrada, F.; Lanz-Mendoza, H. De novo DNA synthesis in Aedes aegypti midgut cells as a complementary strategy to limit dengue viral replication. Front. Microbiol.
**2018**, 9, 801. [Google Scholar] [CrossRef] [Green Version] - Liu, Z.; Zhang, Z.; Lai, Z.; Zhou, T.; Jia, Z.; Gu, J.; Wu, K.; Chen, X.G. Temperature increase enhances Aedes albopictus competence to transmit dengue virus. Front. Microbiol.
**2017**, 8, 2337. [Google Scholar] [CrossRef] [Green Version] - Khoo, C.C.; Piper, J.; Sanchez-Vargas, I.; Olson, K.E.; Franz, A.W. The RNA interference pathway affects midgut infection-and escape barriers for Sindbis virus in Aedes aegypti. BMC Microbiol.
**2010**, 10, 130. [Google Scholar] [CrossRef] [Green Version] - Forrester, N.L.; Guerbois, M.; Seymour, R.L.; Spratt, H.; Weaver, S.C. Vector-borne transmission imposes a severe bottleneck on an RNA virus population. PLoS Pathog.
**2012**, 8, e1002897. [Google Scholar] [CrossRef] - Beaty, B.; Bernhardt, S.; Black, W.; Blair, C.; Eisen, L.; Elizondo-Quiroga, D.; Farfan-Ale, J.; Lozano-Fuentes, S.; Franz, A.; Olson, K.E.; et al. Novel strategies to control Aedes aegypti and dengue. In Vector Biology, Ecology and Control; Springer: New York, NY, USA, 2010; pp. 99–111. [Google Scholar]
- Bisset, J.; Marín, R.; Rodríguez, M.; Severson, D.; Ricardo, Y.; French, L.; Díaz, M.; Pérez, O. Insecticide resistance in two Aedes aegypti (Diptera: Culicidae) strains from Costa Rica. J. Med. Entomol.
**2013**, 50, 352–361. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Singh, R.K.; Dhama, K.; Khandia, R.; Munjal, A.; Karthik, K.; Tiwari, R.; Chakraborty, S.; Malik, Y.S.; Bueno-Marí, R. Prevention and control strategies to counter Zika virus, a special focus on intervention approaches against vector mosquitoes—Current updates. Front. Microbiol.
**2018**, 9, 87. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Fu, G.; Lees, R.S.; Nimmo, D.; Aw, D.; Jin, L.; Gray, P.; Berendonk, T.U.; White-Cooper, H.; Scaife, S.; Phuc, H.K.; et al. Female-specific flightless phenotype for mosquito control. Proc. Natl. Acad. Sci. USA
**2010**, 107, 4550–4554. [Google Scholar] [CrossRef] [Green Version] - Franz, A.W.; Sanchez-Vargas, I.; Raban, R.R.; Black IV, W.C.; James, A.A.; Olson, K.E. Fitness impact and stability of a transgene conferring resistance to dengue-2 virus following introgression into a genetically diverse Aedes aegypti strain. PLoS Negl. Trop. Dis.
**2014**, 8, e2833. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Weaver, S.C. Urbanization and geographic expansion of zoonotic arboviral diseases: Mechanisms and potential strategies for prevention. Trends Microbiol.
**2013**, 21, 360–363. [Google Scholar] [CrossRef] [Green Version] - Tham, H.W.; Balasubramaniam, V.; Ooi, M.K.; Chew, M.F. Viral determinants and vector competence of zika virus transmission. Front. Microbiol.
**2018**, 9, 1040. [Google Scholar] [CrossRef] - Lee, H.C.; Butler, M.; Wu, S.C. Using recombinant DNA technology for the development of live-attenuated dengue vaccines. Enzyme Microb. Technol.
**2012**, 51, 67–72. [Google Scholar] [CrossRef] - Putnak, R.; Barvir, D.A.; Burrous, J.M.; Dubois, D.R.; D’Andrea, V.M.; Hoke, C.H.; Sadoff, J.C.; Eckels, K.H. Development of a purified, inactivated, dengue-2 virus vaccine prototype in Vero cells: Immunogenicity and protection in mice and rhesus monkeys. J. Infect. Dis.
**1996**, 174, 1176–1184. [Google Scholar] [CrossRef] [Green Version] - Tripathi, N.K.; Shrivastava, A. Recent developments in recombinant protein–based Dengue vaccines. Front. Immunol.
**2018**, 9, 1919. [Google Scholar] [CrossRef] - Yauch, L.E.; Shresta, S. Dengue virus vaccine development. In Advances in virus research; Elsevier: Amsterdam, The Netherlands, 2014; Volume 88, pp. 315–372. [Google Scholar]
- Kochel, T.; Wu, S.J.; Raviprakash, K.; Hobart, P.; Hoffman, S.; Porter, K.; Hayes, C. Inoculation of plasmids expressing the dengue-2 envelope gene elicit neutralizing antibodies in mice. Vaccine
**1997**, 15, 547–552. [Google Scholar] [CrossRef] - Aaskov, J.; Buzacott, K.; Thu, H.M.; Lowry, K.; Holmes, E.C. Long-term transmission of defective RNA viruses in humans and Aedes mosquitoes. Science
**2006**, 311, 236–238. [Google Scholar] [CrossRef] [PubMed] - Li, D.; Lott, W.B.; Lowry, K.; Jones, A.; Thu, H.M.; Aaskov, J. Defective interfering viral particles in acute dengue infections. PLoS ONE
**2011**, 6, e19447. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Racaniello, V.R. Picornaviridae, The virus and their replication. In Fields Virol; Fields, B., Knipe, D.M., Howley, P.M., Eds.; Lippincott-Williams & Wilkins: New York, NY, USA, 2006; pp. 795–838. [Google Scholar]
- Nichol, S.; O’Hara, P.; Holland, J.; Perrault, J. Structure and origin of a novel class of defective interfering particle of vesicular stomatitis virus. Nucl. Acids Res.
**1984**, 12, 2775–2790. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Huang, A.S.; Baltimore, D. Defective viral particles and viral disease processes. Nature
**1970**, 226, 325. [Google Scholar] [CrossRef] [PubMed] - Huang, A.S.; Baltimore, D. Defective interfering animal viruses. In Comprehensive Virology 10; Springer: New York, NY, USA, 1977; pp. 73–116. [Google Scholar]
- Barrett, A.T.; Dimmock, N. Defective interfering viruses and infections of animals. In Current Topics in Microbiology and Immunology; Springer: New York, NY, USA, 1986; pp. 55–84. [Google Scholar]
- Kirkwood, T.; Bangham, C. Cycles, chaos, and evolution in virus cultures: A model of defective interfering particles. Proc. Natl. Acad. Sci. USA
**1994**, 91, 8685–8689. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Frank, S.A. Within-host spatial dynamics of viruses and defective interfering particles. J. Theor. Biol.
**2000**, 206, 279–290. [Google Scholar] [CrossRef] [Green Version] - Mapder, T.; Clifford, S.; Aaskov, J.; Burrage, K. A population of bang-bang switches of defective interfering particles makes within-host dynamics of dengue virus controllable. PLoS Comput. Biol.
**2019**, 15, e1006668. [Google Scholar] [CrossRef] [Green Version] - Nguyen, N.M.; Kien, D.T.H.; Tuan, T.V.; Quyen, N.T.H.; Tran, C.N.; Thi, L.V.; Le Thi, D.; Nguyen, H.L.; Farrar, J.J.; Holmes, E.C.; et al. Host and viral features of human dengue cases shape the population of infected and infectious Aedes aegypti mosquitoes. Proc. Natl. Acad. Sci. USA
**2013**, 110, 9072–9077. [Google Scholar] [CrossRef] [Green Version] - Muszkiewicz, A.; Britton, O.J.; Gemmell, P.; Passini, E.; Sánchez, C.; Zhou, X.; Carusi, A.; Quinn, T.A.; Burrage, K.; Bueno-Orovio, A.; et al. Variability in cardiac electrophysiology: Using experimentally-calibrated populations of models to move beyond the single virtual physiological human paradigm. Prog. Biophys. Mol. Biol.
**2016**, 120, 115–127. [Google Scholar] [CrossRef] [Green Version] - Smit, J.; Moesker, B.; Rodenhuis-Zybert, I.; Wilschut, J. Flavivirus cell entry and membrane fusion. Viruses
**2011**, 3, 160–171. [Google Scholar] [CrossRef] [Green Version] - Alen, M.M.; Schols, D. Dengue virus entry as target for antiviral therapy. J. Trop. Med.
**2012**, 2012. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ke, R.; Aaskov, J.; Holmes, E.C.; Lloyd-Smith, J.O. Phylodynamic analysis of the emergence and epidemiological impact of transmissible defective dengue viruses. PLoS Pathog.
**2013**, 9, e1003193. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rodrigues, H.S.; Monteiro, M.T.T.; Torres, D.F. Vaccination models and optimal control strategies to dengue. Math. Biosci.
**2014**, 247, 1–12. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Price, D.J.; Bean, N.G.; Ross, J.V.; Tuke, J. Designing group dose-response studies in the presence of transmission. Math. Biosci.
**2018**, 304, 62–78. [Google Scholar] [CrossRef] - Lydeamore, M.; Campbell, P.; Regan, D.; Tong, S.; Andrews, R.; Steer, A.; Romani, L.; Kaldor, J.; McVernon, J.; McCaw, J. A biological model of scabies infection dynamics and treatment informs mass drug administration strategies to increase the likelihood of elimination. Math. Biosci.
**2019**, 309, 163–173. [Google Scholar] [CrossRef] [Green Version] - Alto, B.W.; Bettinardi, D. Temperature and dengue virus infection in mosquitoes: Independent effects on the immature and adult stages. Am. J. Trop. Med. Hyg.
**2013**, 88, 497–505. [Google Scholar] [CrossRef] - Britton, O.J.; Bueno-Orovio, A.; Van Ammel, K.; Lu, H.R.; Towart, R.; Gallacher, D.J.; Rodriguez, B. Experimentally calibrated population of models predicts and explains intersubject variability in cardiac cellular electrophysiology. Proc. Natl. Acad. Sci. USA
**2013**, 110, E2098–E2105. [Google Scholar] [CrossRef] [Green Version] - Sarkar, A.X.; Christini, D.J.; Sobie, E.A. Exploiting mathematical models to illuminate electrophysiological variability between individuals. J. Physiol.
**2012**, 590, 2555–2567. [Google Scholar] [CrossRef] [Green Version] - Burrage, K.; Burrage, P.M.; Donovan, D.M.; McCourt, T.A.; Thompson, H.B. Estimates on the Coverage of Parameter Space using Populations of Models. Environ. Water Resour. Manag.
**2014**. [Google Scholar] [CrossRef] [Green Version] - Lawson, B.A.; Drovandi, C.C.; Cusimano, N.; Burrage, P.; Rodriguez, B.; Burrage, K. Unlocking data sets by calibrating populations of models to data density: A study in atrial electrophysiology. Sci. Adv.
**2018**, 4, e1701676. [Google Scholar] [CrossRef] [Green Version] - Pontryagin, L.S.; Mishchenko, E.; Boltyanskii, V.; Gamkrelidze, R. The Mathematical Theory of Optimal Processes; Routledge: Abingdon, UK, 1962. [Google Scholar]
- Lenhart, S.; Workman, J.T. Optimal Control Applied to Biological Models; Chapman and Hall/CRC: Boca Raton, FL, USA, 2007. [Google Scholar]
- Sharp, J.A.; Browning, A.P.; Mapder, T.; Burrage, K.; Simpson, M.J. Optimal control of acute myeloid leukaemia. J. Theor. Biol.
**2019**, 470, 30–42. [Google Scholar] [CrossRef] [PubMed] - Lin, J. Divergence measures based on the Shannon entropy. IEEE Trans. Inf. Theory
**1991**, 37, 145–151. [Google Scholar] [CrossRef] [Green Version] - Kullback, S.; Leibler, R.A. On information and sufficiency. Ann. Math. Stat.
**1951**, 22, 79–86. [Google Scholar] [CrossRef] - Duong, V.; Lambrechts, L.; Paul, R.E.; Ly, S.; Lay, R.S.; Long, K.C.; Huy, R.; Tarantola, A.; Scott, T.W.; Sakuntabhai, A.; et al. Asymptomatic humans transmit dengue virus to mosquitoes. Proc. Natl. Acad. Sci. USA
**2015**, 112, 14688–14693. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Dengue virus host-to-vector transmission model: The virus ($V\left(t\right)$) and the defective interfering (DI) particles ($D\left(t\right)$) are transmitted from infected hosts to mosquitoes. The susceptible mosquitoes (S) can be infected by virus or DI particles to generate the two types of infected mosquitoes, ${I}_{V}$ and ${I}_{D}$. Further, a dually-infected population (${I}_{VD}$) is generated from co-infection by $D\left(t\right)$ and $V\left(t\right)$, simultaneously. The model has been considered in two-compartments. The $D\left(t\right)$ and $V\left(t\right)$ are generated in the within-host compartment and infect the mosquito population in the other compartment. For each within-host model (shown in left box), multiple plausible transmission models has been calibrated (shown by multiple lines). The shaded domain indicates the days of high fever.

**Figure 2.**Population of models for infected mosquitoes: The dengue virus infected mosquito data for 408 exposure experiments with 208 hospitalised dengue patients reported in Nguyen et al. [33] are calibrated to construct serotype-specific population of models (POMs). The black scattered points in the top panel represent the fraction of viral infected mosquitoes (${\tilde{I}}_{V}$) observed in the exposure experiment. The group of lines in different colours (in the top, middle and bottom panels) are the calibrated POMs outputs for different patient models in the population.

**Figure 3.**Variability in accepted model parameters: The parameters accepted in the POMs are shown in box plots for the four serotypes. The density of the parameters (A, $\mu $, $\varphi $) are shown in the scatter plots in the background of the box plots.

**Figure 4.**Mosquito infectious dose: The infected mosquitoes by virus (${\tilde{I}}_{V}$) and DI particles (${\tilde{I}}_{D}$) are shown in scattered plots with respect to the ${\mathrm{Log}}_{10}$ values of corresponding within-host virus ($V\left(t\right)$) and DI particles ($D\left(t\right)$) levels. Different colours represent different patient models. These scatter plots represent the phase portrait of the data shown in Figure 2 versus the viraemia data reported in our previous model [32] and is a way to estimate the ranges of different mosquito infectious doses ($MID$s), say $MI{D}_{50}$.

**Figure 5.**Controlled population of transmission models: Each serotype-specific POMs (from Figure 2) are considered after applying optimal bang-bang control to construct the controlled POMs (cPOMs). The infected mosquitoes by virus only (${\tilde{I}}_{VC}$), by DI only (${\tilde{I}}_{DC}$) and by both (${\tilde{I}}_{VDC}$), are computed by using the controlled within-host plasma viraemias in the populations for four dengue serotypes.

**Figure 6.**Controlled MIDs: Scatter plots show the controlled infected fractions (${I}_{VC}$ and ${I}_{DC}$) of the mosquito population versus the controlled patient viraemias ($V\left(t\right)$ and $D\left(t\right)$). The transmission of DI particles with respect to the ${\mathrm{Log}}_{10}$ values of the plasma DI particles ($D\left(t\right)$) has notable rise after applying the control (see Figure 4).

**Figure 7.**Control efficiency: The reduction in the human-to-mosquito virus transmission was evaluated by Jensen-Shannon (J-S) divergence ($\mathcal{D}$), calculated between the distributions of the virus infected mosquitoes before (${\tilde{I}}_{V}$) and after (${\tilde{I}}_{VC}$) applying the optimal control. The box plot for each serotype explains the variation in the J-S divergence on each day of the febrile period (in the insets). The main scatter plot compares the efficiency of the applied optimal controls for different serotypes, in terms of J-S divergence versus normalised control expense (C) (red: DENV-1, blue: DENV-2, green: DENV-3, cyan: DENV-4). The control expense was computed by the area under the control curve [32].

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**MDPI and ACS Style**

Mapder, T.; Aaskov, J.; Burrage, K.
Administration of Defective Virus Inhibits Dengue Transmission into Mosquitoes. *Viruses* **2020**, *12*, 558.
https://doi.org/10.3390/v12050558

**AMA Style**

Mapder T, Aaskov J, Burrage K.
Administration of Defective Virus Inhibits Dengue Transmission into Mosquitoes. *Viruses*. 2020; 12(5):558.
https://doi.org/10.3390/v12050558

**Chicago/Turabian Style**

Mapder, Tarunendu, John Aaskov, and Kevin Burrage.
2020. "Administration of Defective Virus Inhibits Dengue Transmission into Mosquitoes" *Viruses* 12, no. 5: 558.
https://doi.org/10.3390/v12050558