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Liyanage YR, Heitzman-Breen N, Tuncer N, Ciupe SM. Identifiability investigation of within-host models of acute virus infection. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.05.09.593464. [PMID: 38766177 PMCID: PMC11100786 DOI: 10.1101/2024.05.09.593464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2024]
Abstract
Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we use four mathematical models of influenza A infection with increased degrees of biological realism. We test the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refine the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we present insight into the sources of uncertainty in parameter estimation and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.
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Affiliation(s)
- Yuganthi R Liyanage
- Department of Mathematics and Statistics, Florida Atlantic University, Boca Raton, FL, USA
| | - Nora Heitzman-Breen
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Necibe Tuncer
- Department of Mathematics and Statistics, Florida Atlantic University, Boca Raton, FL, USA
| | - Stanca M Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
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Timsina AN, Liyanage YR, Martcheva M, Tuncer N. A novel within-host model of HIV and nutrition. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:5577-5603. [PMID: 38872549 DOI: 10.3934/mbe.2024246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ \mathcal{R}_0 < 1 $, and unstable when $ \mathcal{R}_0 > 1 $. The infection equilibrium is locally asymptotically stable if $ \mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.
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Affiliation(s)
- Archana N Timsina
- Department of Population Health and Pathobiology, North Carolina State University, Raleigh 27607, USA
| | - Yuganthi R Liyanage
- Department of Mathematical Sciences, Florida Atlantic University, Boca Raton 33431, USA
| | - Maia Martcheva
- Department of Mathematics, University of Florida, Gainesville 32611, USA
| | - Necibe Tuncer
- Department of Mathematical Sciences, Florida Atlantic University, Boca Raton 33431, USA
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3
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Zitzmann C, Ke R, Ribeiro RM, Perelson AS. How robust are estimates of key parameters in standard viral dynamic models? PLoS Comput Biol 2024; 20:e1011437. [PMID: 38626190 PMCID: PMC11051641 DOI: 10.1371/journal.pcbi.1011437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Revised: 04/26/2024] [Accepted: 04/01/2024] [Indexed: 04/18/2024] Open
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.
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Affiliation(s)
- Carolin Zitzmann
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
| | - Ruian Ke
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
| | - Ruy M. Ribeiro
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
| | - Alan S. Perelson
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
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Johnson RM, Stopard IJ, Byrne HM, Armstrong PM, Brackney DE, Lambert B. Investigating the dose-dependency of the midgut escape barrier using a mechanistic model of within-mosquito dengue virus population dynamics. PLoS Pathog 2024; 20:e1011975. [PMID: 38557892 PMCID: PMC11008821 DOI: 10.1371/journal.ppat.1011975] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Revised: 04/11/2024] [Accepted: 01/16/2024] [Indexed: 04/04/2024] Open
Abstract
Arboviruses can emerge rapidly and cause explosive epidemics of severe disease. Some of the most epidemiologically important arboviruses, including dengue virus (DENV), Zika virus (ZIKV), Chikungunya (CHIKV) and yellow fever virus (YFV), are transmitted by Aedes mosquitoes, most notably Aedes aegypti and Aedes albopictus. After a mosquito blood feeds on an infected host, virus enters the midgut and infects the midgut epithelium. The virus must then overcome a series of barriers before reaching the mosquito saliva and being transmitted to a new host. The virus must escape from the midgut (known as the midgut escape barrier; MEB), which is thought to be mediated by transient changes in the permeability of the midgut-surrounding basal lamina layer (BL) following blood feeding. Here, we present a mathematical model of the within-mosquito population dynamics of DENV (as a model system for mosquito-borne viruses more generally) that includes the interaction of the midgut and BL which can account for the MEB. Our results indicate a dose-dependency of midgut establishment of infection as well as rate of escape from the midgut: collectively, these suggest that the extrinsic incubation period (EIP)-the time taken for DENV virus to be transmissible after infection-is shortened when mosquitoes imbibe more virus. Additionally, our experimental data indicate that multiple blood feeding events, which more closely mimic mosquito-feeding behavior in the wild, can hasten the course of infections, and our model predicts that this effect is sensitive to the amount of virus imbibed. Our model indicates that mutations to the virus which impact its replication rate in the midgut could lead to even shorter EIPs when double-feeding occurs. Mechanistic models of within-vector viral infection dynamics provide a quantitative understanding of infection dynamics and could be used to evaluate novel interventions that target the mosquito stages of the infection.
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Affiliation(s)
- Rebecca M. Johnson
- Center for Vector-Borne and Zoonotic Diseases, Department of Entomology, The Connecticut Agricultural Experiment Station, New Haven, Connecticut, United States of America
| | - Isaac J. Stopard
- MRC Centre for Global Infectious Disease Analysis, School of Public Health, Faculty of Medicine, Imperial College London, London, United Kingdom
| | - Helen M. Byrne
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Philip M. Armstrong
- Center for Vector-Borne and Zoonotic Diseases, Department of Entomology, The Connecticut Agricultural Experiment Station, New Haven, Connecticut, United States of America
| | - Douglas E. Brackney
- Center for Vector-Borne and Zoonotic Diseases, Department of Entomology, The Connecticut Agricultural Experiment Station, New Haven, Connecticut, United States of America
| | - Ben Lambert
- Department of Statistics, University of Oxford, Oxford, United Kingdom
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Sreejithkumar V, Ghods K, Bandara T, Martcheva M, Tuncer N. Modeling the interplay between albumin-globulin metabolism and HIV infection. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:19527-19552. [PMID: 38052613 DOI: 10.3934/mbe.2023865] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
Human immunodeficiency virus (HIV) infection is a major public health concern with 1.2 million people living with HIV in the United States. The role of nutrition in general, and albumin/globulin in particular in HIV progression has long been recognized. However, no mathematical models exist to describe the interplay between HIV and albumin/globulin. In this paper, we present a family of models of HIV and the two protein components albumin and globulin. We use albumin, globulin, viral load and target cell data from simian immunodeficiency virus (SIV)-infected monkeys to perform model selection on the family of models. We discover that the simplest model accurately and uniquely describes the data. The selection of the simplest model leads to the observation that albumin and globulin do not impact the infection rate of target cells by the virus and the clearance of the infected target cells by the immune system. Moreover, the recruitment of target cells and immune cells are modeled independently of globulin in the selected model. Mathematical analysis of the selected model reveals that the model has an infection-free equilibrium and a unique infected equilibrium when the immunological reproduction number is above one. The infection-free equilibrium is locally stable when the immunological reproduction number is below one, and unstable when the immunological reproduction number is greater than one. The infection equilibrium is locally stable whenever it exists. To determine the parameters of the best fitted model we perform structural and practical identifiability analysis. The structural identifiability analysis reveals that the model is identifiable when the immune cell infection rate is fixed at a value obtained from the literature. Practical identifiability reveals that only seven of the sixteen parameters are practically identifiable with the given data. Practical identifiability of parameters performed with synthetic data sampled a lot more frequently reveals that only two parameters are practically unidentifiable. We conclude that experiments that will improve the quality of the data can help improve the parameter estimates and lead to better understanding of the interplay of HIV and albumin-globulin metabolism.
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Affiliation(s)
- Vivek Sreejithkumar
- Florida Atlantic University, Department of Mathematical Sciences, Boca Raton, FL 33431, USA
| | - Kia Ghods
- Florida Atlantic University, Department of Mathematical Sciences, Boca Raton, FL 33431, USA
| | - Tharusha Bandara
- University of Florida, Department of Mathematics, Gainesville, FL 32611, USA
| | - Maia Martcheva
- University of Florida, Department of Mathematics, Gainesville, FL 32611, USA
| | - Necibe Tuncer
- Florida Atlantic University, Department of Mathematical Sciences, Boca Raton, FL 33431, USA
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Johnson RM, Stopard IJ, Byrne HM, Armstrong PM, Brackney DE, Lambert B. Investigating the dose-dependency of the midgut escape barrier using a mechanistic model of within-mosquito dengue virus population dynamics. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.09.28.559904. [PMID: 37808804 PMCID: PMC10557669 DOI: 10.1101/2023.09.28.559904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/10/2023]
Abstract
Flaviviruses are arthropod-borne (arbo)viruses which can emerge rapidly and cause explosive epidemics of severe disease. Some of the most epidemiologically important flaviviruses, including dengue virus (DENV), Zika virus (ZIKV) and yellow fever virus (YFV), are transmitted by Aedes mosquitoes, most notably Aedes aegypti and Aedes albopictus. After a mosquito blood feeds on an infected host, virus enters the midgut and infects the midgut epithelium. The virus must then overcome a series of barriers before reaching the mosquito saliva and being transmitted to a new host. The virus must escape from the midgut (known as the midgut escape barrier; MEB), which is thought to be mediated by transient changes in the permeability of the midgut-surrounding basal lamina layer (BL) following blood feeding. Here, we present a mathematical model of the within-mosquito population dynamics of flaviviruses that includes the interaction of the midgut and BL which can account for the MEB. Our results indicate a dose-dependency of midgut establishment of infection as well as rate of escape from the midgut: collectively, these suggest that the extrinsic incubation period (EIP) - the time taken for DENV virus to be transmissible after infection - is shortened when mosquitoes imbibe more virus. Additionally, our experimental data indicates that multiple blood feeding events, which more closely mimic mosquito-feeding behavior in the wild, can hasten the course of infections, and our model predicts that this effect is sensitive to the amount of virus imbibed. Our model indicates that mutations to the virus which impact its replication rate in the midgut could lead to even shorter EIPs when double-feeding occurs. Mechanistic models of within-vector viral infection dynamics provide a quantitative understanding of infection dynamics and could be used to evaluate novel interventions that target the mosquito stages of the infection. Author summary Aedes mosquitoes are the main vectors of dengue virus (DENV), Zika virus (ZIKV) and yellow fever virus (YFV), all of which can cause severe disease in humans with dengue alone infecting an estimated 100-400 million people each year. Understanding the processes that affect whether, and at which rate, mosquitoes may transmit such viruses is, hence, paramount. Here, we present a mathematical model of virus dynamics within infected mosquitoes. By combining the model with novel experimental data, we show that the course of infection is sensitive to the initial dose of virus ingested by the mosquito. The data also indicates that mosquitoes which blood feed subsequent to becoming infected may be able to transmit infection earlier, which is reproduced in the model. This is important as many mosquito species feed multiple times during their lifespan and, any reduction in time to dissemination will increase the number of days that a mosquito is infectious and so enhance the risk of transmission. Our study highlights the key and complementary roles played by mathematical models and experimental data for understanding within-mosquito virus dynamics.
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Cavany SM, Barbera C, Carpenter M, Rodgers C, Sherman T, Stenglein M, Mayo C, Perkins TA. Modeling cellular co-infection and reassortment of bluetongue virus in Culicoides midges. Virus Evol 2022; 8:veac094. [PMID: 36381232 PMCID: PMC9662319 DOI: 10.1093/ve/veac094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Revised: 09/21/2022] [Accepted: 09/29/2022] [Indexed: 10/10/2023] Open
Abstract
When related segmented RNA viruses co-infect a single cell, viral reassortment can occur, potentially leading to new strains with pandemic potential. One virus capable of reassortment is bluetongue virus (BTV), which causes substantial health impacts in ruminants and is transmitted via Culicoides midges. Because midges can become co-infected by feeding on multiple different host species and remain infected for their entire life span, there is a high potential for reassortment to occur. Once a midge is co-infected, additional barriers must be crossed for a reassortant virus to emerge, such as cellular co-infection and dissemination of reassortant viruses to the salivary glands. We developed three mathematical models of within-midge BTV dynamics of increasing complexity, allowing us to explore the conditions leading to the emergence of reassortant viruses. In confronting the simplest model with published data, we estimate that the average life span of a bluetongue virion in the midge midgut is about 6 h, a key determinant of establishing a successful infection. Examination of the full model, which permits cellular co-infection and reassortment, shows that small differences in fitness of the two infecting strains can have a large impact on the frequency with which reassortant virions are observed. This is consistent with experimental co-infection studies with BTV strains with different relative fitnesses that did not produce reassortant progeny. Our models also highlight several gaps in existing data that would allow us to elucidate these dynamics in more detail, in particular the times it takes the virus to disseminate to different tissues, and measurements of viral load and reassortant frequency at different temperatures.
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Affiliation(s)
- Sean M Cavany
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Carly Barbera
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
| | - Molly Carpenter
- Microbiology, Immunology, and Pathology Department, Colorado State University, Fort Collins, CO 80523, USA
| | - Case Rodgers
- Microbiology, Immunology, and Pathology Department, Colorado State University, Fort Collins, CO 80523, USA
| | - Tyler Sherman
- Microbiology, Immunology, and Pathology Department, Colorado State University, Fort Collins, CO 80523, USA
| | - Mark Stenglein
- Microbiology, Immunology, and Pathology Department, Colorado State University, Fort Collins, CO 80523, USA
| | - Christie Mayo
- Microbiology, Immunology, and Pathology Department, Colorado State University, Fort Collins, CO 80523, USA
| | - T Alex Perkins
- Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA
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Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans. Sci Rep 2022; 12:14637. [PMID: 36030320 PMCID: PMC9418662 DOI: 10.1038/s41598-022-18683-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2022] [Accepted: 08/16/2022] [Indexed: 12/12/2022] Open
Abstract
Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we developed a novel two-patch within-host mathematical model that considered the infection of both respiratory tracts and assumed that the viral load in the lower respiratory tract decays in a density dependent manner and investigated its ability to match population level data. We proposed several approaches that can improve practical identifiability of parameters, including an optimal experimental approach, and found that availability of viral data early in the infection is of essence for improving the accuracy of the estimates. Our findings can be useful for designing interventions.
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