How robust are estimates of key parameters in standard viral dynamic models?

Abstract

Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

“…Since we do not know the time of infection and estimating the time of infection without data during the early phase of infection is problematic due to model identifiability issues [ 55 , 56 ], we fixed the duration from infection to symptom onset to 5 days as in previous studies [ 34 , 57 , 58 ]. This assumption is based on estimates that the duration from exposure to symptom onset is about 5 days [ 24 , 59 – 62 ].…”

“…where -2LL is the -2 times loglikelihood, dim θ R is the number of the random and fixed covariate parameters, N is the number of subjects, dim (θ F ) is the number of fixed effects (except covariates), and n tot is the total number of observations (Monolix.lixoft.com/tasks/loglikelihood-estimation). Since we do not know the time of infection and estimating the time of infection without data during the early phase of infection is problematic due to model identifiability issues [55,56], we fixed the duration from infection to symptom onset to 5 days as in previous studies [34,57,58]. This assumption is based on estimates that the duration from exposure to symptom PLOS PATHOGENS onset is about 5 days [24,[59][60][61][62].…”