Data-driven models for replication kinetics of Orthohantavirus infections

Abstract

The Hantaviridae constitute a family of viruses harbored by mice, rats, shrews, voles, moles and bats. Intriguingly, only viruses harbored by mice and rats may cause disease in humans with up to 40% case fatality rate in the Americas. Transmission of virus from rodents to humans occurs via the respiratory route and results in replication of the virus in the microvascular endothelial cells of the lung or kidney. Understanding the replication kinetics of these viruses in various cell types and how replication is abrogated by the host is critical to the development of effective therapeutics for treatment for which there are none. We formulate several new ordinary differential equation (ODE) models to examine the replication kinetics of Prospect Hill orthohantavirus (PHV). The models are distinguished by the distribution of the viral replication delay. A new threshold, R_GE, the genome equivalent replication number, is defined in terms of the model parameters. New final density relations are derived that associate R_GE to the asymptotic number of virions in each model. All models are fit to real time (qRT)-PCR data of genomic RNA from PHV released from Vero E6 cells over 192 h. A sensitivity analysis of the parameters is performed and models are tested for best fit. Our findings provide a basis for future research into formulating more complex mathematical models for evaluation of the replication of hantaviruses in various cell types and sources.

Keywords: Final density relation; In vitro data; Orthohantavirus; Within-host.

Fig. B.1.

Erlang densities for the time delay before budding in the models with n = 1, 2, 3, 4 latent stages. Parameter values are given in Table 2.

Fig. C.2.

Monotonicity plots of virions at t = 192 hpi and 10,000 iterations using the parameter estimates in Table 2 for the models with n = 1, 2, 3, 4 latent stages, plots (a), (b), (c), (d), respectively. The x-axis range is [0.5p, 1.5p], where p is the best fit parameter.

Fig. 1.

Compartmental diagram of interactions between healthy target cells (T), latent cells (L_i, i = 1, …, n), actively infected cells (I), and virions (V). Target cells become latent cells at a rate βTV. Latent cells transition between stages, L_i → L_i+1, at a rate nkL_i, i = 1, …, n − 1, and to infected cells, L_n → I, at a rate nkL_n. Infected cells go into stasis at a rate δI and virions bud off infected cells at a rate bI.

Fig. 2.

Numerical solutions of the n = 1, 2, 3 ,4 latent stage models using the best fit parameters (Table 2). The 23 data points corresponding to the GE are plotted with circles.