# Evaluating the Within-Host Dynamics of Ranavirus Infection with Mechanistic Disease Models and Experimental Data

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*Iridoviridae*: Molecular and Ecological Studies of a Family Infecting Invertebrates and Ectothermic Vertebrates)

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Assessment of Within-Host Ranaviral Dynamics

^{5}plaque-forming units [pfu] mL

^{−1}; n = 150), medium-dose (10

^{3}pfu mL

^{−1}; n = 150), or a low, but unknown dose (n = 90 in “mock” exposure to inadvertently contaminated cell culture media). The tadpoles were assigned to be euthanized and sampled on days 2, 4, 6, 8, 14, 21, 28, 35, 42, and 49 post exposure (n = 15 high-dose, n = 15 low-dose, and n = 9 “mock” tadpoles per time point), although some died and were sampled before their assigned date. Viral titers in liver and kidney samples were measured with a quantitative real-time PCR assay [19].

#### 2.2. Mechanistic Models of Within-Host Dynamics

#### 2.3. Fitting the Models to the Experimental Data

#### 2.4. Model Comparisons

## 3. Results

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**The fit of model B2 to the experimental data. Circles are data points representing the viral DNA copies from individual bullfrog tadpoles that were sampled on a given day. The median model fit (solid red line) and 95% Bayesian credible interval (CI) of the fit (dashed red lines) are shown. Additionally, the median (dashed vertical line) and 95% CI (light red polygon) are shown for the time of the maximum viral titer predicted by the model.

**Table 1.**Model structures and model comparisons. The bolded model (B2) is the most parsimonious based on LOO-IC selection and the lower number of parameters compared to B3.

Class | ID | Structure | Notes | Penalty (pLOO) | LOO-IC | ΔLOO-IC |
---|---|---|---|---|---|---|

A | A1 | ${V}^{\prime}=\varphi V-\text{}\beta VZ$ ${Z}^{\prime}=\psi Z\frac{V}{\left(V+\gamma \right)}$ | Drives virus extinct. $Z$ goes to equilibrium ${Z}_{(\infty )}$, which is above ${Z}_{\left(0\right)}$. | 8.5 | 782.9 | 15.5 |

A2 | ${V}^{\prime}=\varphi V\left(1-\frac{V}{K}\right)-\text{}\beta VZ$ ${Z}^{\prime}=\psi Z\frac{V}{\left(V+\gamma \right)}$ | Conditions under which virus goes to carrying capacity. Or virus goes extinct. | 7.1 | 811.7 | 44.3 | |

B | B1 | ${V}^{\prime}=\varphi V-\text{}\beta VZ$ ${Z}^{\prime}=({N}_{Z}-\delta Z)+\text{}\psi ZV$ | Damped oscillations to a stable point equilibrium, where virus is persistent in host. The model fit shows several oscillations before equilibrium. | 12.7 | 826.6 | 59.2 |

B2 | ${V}^{\prime}=\varphi V-\text{}\beta VZ$ ${Z}^{\prime}=({N}_{Z}-\delta Z)+\text{}\psi Z\frac{V}{\left(V+\gamma \right)}$ | Spike in viral load, then decline to stable point equilibrium, where virus is persistent in host. | 10.1 | 768.6 | 1.2 | |

B3 | ${V}^{\prime}=\varphi V\left(1-\frac{V}{K}\right)-\text{}\beta VZ$ ${Z}^{\prime}=({N}_{Z}-\delta Z)+\text{}\psi Z\frac{V}{\left(V+\gamma \right)}$ | Over-fitting. Extra parameter (carrying capacity, K) unnecessary. | 9.1 | 767.4 | 0 |

**Table 2.**Parameter estimates (median and 95% credible intervals) from the most parsimonious model, B2.

Parameter | Description | Units | Estimate |
---|---|---|---|

$V\left(0\right)$ low | Initial viral densities (per dosage) | Viral DNA copy (VC) | 0.12 (0.01–0.89) |

$V\left(0\right)$ medium | 1.47 (0.24–11.55) | ||

$V\left(0\right)$ high | 24.10 (5.31–146.85) | ||

$Z\left(0\right)$ | Initial immune component denisty | Immune component (IC) | 0.35 (0.04–4.43) |

$\varphi $ | Viral replication rate | day^{−1} | 2.39 (1.07–4.63) |

$\beta $ | Mass-action attack rate | (IC)^{−1} day^{−1} | 1.75 (0.15–6.28) |

${N}_{Z}$ | Rate of production that ensures return of immune system to homeostasis | (IC) day^{−1} | ${N}_{Z}=\delta Z\left(0\right)$ |

$\delta $ | Rate of decline that ensures return of immune system to homeostasis | day^{−1} | 1.29 (0.41–3.92) |

$\psi $ | Immune component growth rate in response to virus | day^{−1} | 0.99 (0.19–3.56) |

$\gamma $ | Half saturation constant | VC | 0.13 (0.02–1.02) |

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**MDPI and ACS Style**

Mihaljevic, J.R.; Greer, A.L.; Brunner, J.L.
Evaluating the Within-Host Dynamics of *Ranavirus* Infection with Mechanistic Disease Models and Experimental Data. *Viruses* **2019**, *11*, 396.
https://doi.org/10.3390/v11050396

**AMA Style**

Mihaljevic JR, Greer AL, Brunner JL.
Evaluating the Within-Host Dynamics of *Ranavirus* Infection with Mechanistic Disease Models and Experimental Data. *Viruses*. 2019; 11(5):396.
https://doi.org/10.3390/v11050396

**Chicago/Turabian Style**

Mihaljevic, Joseph R., Amy L. Greer, and Jesse L. Brunner.
2019. "Evaluating the Within-Host Dynamics of *Ranavirus* Infection with Mechanistic Disease Models and Experimental Data" *Viruses* 11, no. 5: 396.
https://doi.org/10.3390/v11050396