1
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El Messaoudi S, Brichler S, Fougerou-Leurent C, Gordien E, Gerber A, Kortebi A, Lagadic G, Subic-Levrero M, Metivier S, Pol S, Minello A, Ratziu V, Leroy V, Mathurin P, Alric L, Coulibaly F, Pawlotsky JM, Zoulim F, de Lédinghen V, Guedj J. Effect of Peg-IFN on the viral kinetics of patients with HDV infection treated with bulevirtide. JHEP Rep 2024; 6:101070. [PMID: 39100818 PMCID: PMC11295569 DOI: 10.1016/j.jhepr.2024.101070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 01/30/2024] [Revised: 03/12/2024] [Accepted: 03/14/2024] [Indexed: 08/06/2024] Open
Abstract
Background & Aims Bulevirtide is a first-in-class entry inhibitor antiviral treatment for chronic hepatitis D. The viral kinetics during bulevirtide therapy and the effect of combining bulevirtide with pegylated-interferon (Peg-IFN) are unknown. Methods We used mathematical modelling to analyze the viral kinetics in two French observational cohorts of 183 patients receiving bulevirtide with or without Peg-IFN for 48 weeks. Results The efficacy of bulevirtide in blocking cell infection was estimated to 90.3%, whereas Peg-IFN blocked viral production with an efficacy of 92.4%, albeit with large inter-individual variabilities. The addition of Peg-IFN to bulevirtide was associated with a more rapid virological decline, with a rate of virological response (>2 log of decline or undetectability) at week 48 of 86.9% (95% prediction interval [PI] = [79.7-95.0]), compared with 56.1% (95% PI = [46.4-66.7]) with bulevirtide only. The model was also used to predict the probability to achieve a cure of viral infection, with a rate of 8.8% (95% PI = [3.5-13.2]) with bulevirtide compared with 18.8% (95% PI = [11.6-29.0]) with bulevirtide + Peg-IFN. Mathematical modelling suggests that after 144 weeks of treatment, the rates of viral cure could be 42.1% (95% PI = [33.3-52.6]) with bulevirtide and 66.7% (95% PI = [56.5-76.8]) with bulevirtide + Peg-IFN. Conclusions In this analysis of real-world data, Peg-IFN strongly enhanced the kinetics of viral decline in patients treated with bulevirtide. Randomized clinical trials are warranted to assess the virological and clinical benefit of this combination, and to identify predictors of poor response to treatment. Impact and implications Bulevirtide has been approved for chronic HDV infection by regulatory agencies in Europe based on its good safety profile and rapid virological response after treatment initiation, but the optimal duration of treatment and the chance to achieve a sustained virological response remain unknown. The results presented in this study have a high impact for clinicians and investigators as they provide important knowledge on the long-term virological benefits of a combination of Peg-IFN and bulevirtide in patients with CHD. Clinical trials are now warranted to confirm those predictions.
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Affiliation(s)
| | - Ségolène Brichler
- National Reference Center for Viral Hepatitis B, C, and D, Department of Clinical Microbiology, Hôpital Avicenne AP-HP, Université Sorbonne Paris Nord, Bobigny, INSERM U955, Créteil, France
| | - Claire Fougerou-Leurent
- Clinical Pharmacology Department, CHU Rennes, Rennes, France
- CIC 1414 (Clinical Investigation Center), INSERM, Rennes, France
| | - Emmanuel Gordien
- National Reference Center for Viral Hepatitis B, C, and D, Department of Clinical Microbiology, Hôpital Avicenne AP-HP, Université Sorbonne Paris Nord, Bobigny, INSERM U955, Créteil, France
| | - Athenaïs Gerber
- National Reference Center for Viral Hepatitis B, C, and D, Department of Clinical Microbiology, Hôpital Avicenne AP-HP, Université Sorbonne Paris Nord, Bobigny, INSERM U955, Créteil, France
| | - Amal Kortebi
- Clinical Pharmacology Department, CHU Rennes, Rennes, France
- CIC 1414 (Clinical Investigation Center), INSERM, Rennes, France
| | - Garance Lagadic
- Clinical Pharmacology Department, CHU Rennes, Rennes, France
- CIC 1414 (Clinical Investigation Center), INSERM, Rennes, France
| | - Miroslava Subic-Levrero
- Department of Hepatology, Hospices Civils de Lyon, INSERM Unit 1052, Université Claude Bernard Lyon 1, France
| | | | - Stanislas Pol
- Department of Hepatology, Hôpital Cochin, AP-HP, Université Paris-René Descartes, INSERM U1016, Paris, France
| | - Anne Minello
- Department of Hepatology and Gastroenterology, University hospital Dijon, INSERM UMR 1231, France
| | - Vlad Ratziu
- Sorbonne Université, Assistance Publique-Hôpitaux de Paris, Hôpital Pitié Salpêtrière, Institute of Cardiometabolism and Nutrition (ICAN), Paris, France
| | - Vincent Leroy
- Department of Hepatology and Gastroenterology, Centre Hospitalo-Universitaire, INSERM U1209, Université Grenoble Alpes, Grenoble, France
| | - Philippe Mathurin
- Service des maladies de l’appareil digestif, Université Lille 2 and Inserm U795, Lille, France
| | - Laurent Alric
- Department of Internal Medicine and Digestive Diseases, UMR-152, Toulouse III University, Toulouse, France
| | - Fatoumata Coulibaly
- Clinical research department, ANRS Maladies infectieuses émergentes, Paris, France
| | - Jean-Michel Pawlotsky
- National Reference Center for Viral Hepatitis B, C, and D, Department of Virology, Hôpital Henri Mondor, Université Paris-Est, Inserm U955, Créteil, France
| | - Fabien Zoulim
- Department of Hepatology, Hospices Civils de Lyon, INSERM Unit 1052, Université Claude Bernard Lyon 1, France
| | - Victor de Lédinghen
- Centre d'Investigation de la Fibrose Hépatique, Bordeaux University Hospital, Pessac, France; INSERM U1312, Bordeaux University, Bordeaux, France
| | | | - the ANRS HD EP01 BULEDELTA Study Group
- Université Paris Cité, IAME, Inserm, Paris, France
- National Reference Center for Viral Hepatitis B, C, and D, Department of Clinical Microbiology, Hôpital Avicenne AP-HP, Université Sorbonne Paris Nord, Bobigny, INSERM U955, Créteil, France
- Clinical Pharmacology Department, CHU Rennes, Rennes, France
- CIC 1414 (Clinical Investigation Center), INSERM, Rennes, France
- Department of Hepatology, Hospices Civils de Lyon, INSERM Unit 1052, Université Claude Bernard Lyon 1, France
- Department of Hepatology, CHU Rangueil, Toulouse, France
- Department of Hepatology, Hôpital Cochin, AP-HP, Université Paris-René Descartes, INSERM U1016, Paris, France
- Department of Hepatology and Gastroenterology, University hospital Dijon, INSERM UMR 1231, France
- Sorbonne Université, Assistance Publique-Hôpitaux de Paris, Hôpital Pitié Salpêtrière, Institute of Cardiometabolism and Nutrition (ICAN), Paris, France
- Department of Hepatology and Gastroenterology, Centre Hospitalo-Universitaire, INSERM U1209, Université Grenoble Alpes, Grenoble, France
- Service des maladies de l’appareil digestif, Université Lille 2 and Inserm U795, Lille, France
- Department of Internal Medicine and Digestive Diseases, UMR-152, Toulouse III University, Toulouse, France
- Clinical research department, ANRS Maladies infectieuses émergentes, Paris, France
- National Reference Center for Viral Hepatitis B, C, and D, Department of Virology, Hôpital Henri Mondor, Université Paris-Est, Inserm U955, Créteil, France
- Centre d'Investigation de la Fibrose Hépatique, Bordeaux University Hospital, Pessac, France; INSERM U1312, Bordeaux University, Bordeaux, France
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2
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Ciupe SM, Dahari H, Ploss A. Mathematical Models of Early Hepatitis B Virus Dynamics in Humanized Mice. Bull Math Biol 2024; 86:53. [PMID: 38594319 PMCID: PMC11003933 DOI: 10.1007/s11538-024-01284-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 03/15/2024] [Indexed: 04/11/2024]
Abstract
Analyzing the impact of the adaptive immune response during acute hepatitis B virus (HBV) infection is essential for understanding disease progression and control. Here we developed mathematical models of HBV infection which either lack terms for adaptive immune responses, or assume adaptive immune responses in the form of cytolytic immune killing, non-cytolytic immune cure, or non-cytolytic-mediated block of viral production. We validated the model that does not include immune responses against temporal serum hepatitis B DNA (sHBV) and temporal serum hepatitis B surface-antigen (HBsAg) experimental data from mice engrafted with human hepatocytes (HEP). Moreover, we validated the immune models against sHBV and HBsAg experimental data from mice engrafted with HEP and human immune system (HEP/HIS). As expected, the model that does not include adaptive immune responses matches the observed high sHBV and HBsAg concentrations in all HEP mice. By contrast, while all immune response models predict reduction in sHBV and HBsAg concentrations in HEP/HIS mice, the Akaike Information Criterion cannot discriminate between non-cytolytic cure (resulting in a class of cells refractory to reinfection) and antiviral block functions (of up to 99 % viral production 1-3 weeks following peak viral load). We can, however, reject cytolytic killing, as it can only match the sHBV and HBsAg data when we predict unrealistic levels of hepatocyte loss.
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Affiliation(s)
- Stanca M Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA.
| | - Harel Dahari
- Division of Hepatology, Department of Medicine, Loyola University, Chicago, IL, USA
| | - Alexander Ploss
- Department of Molecular Biology, Princeton University, Princeton, NJ, USA
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3
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Zhang Z, Liang G, Chang K. Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by the Ornstein-Uhlenbeck process. PLoS One 2023; 18:e0292073. [PMID: 37773949 PMCID: PMC10540978 DOI: 10.1371/journal.pone.0292073] [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: 05/11/2023] [Accepted: 09/12/2023] [Indexed: 10/01/2023] Open
Abstract
A reaction-diffusion hepatitis B virus (HBV) infection model based on the mean-reverting Ornstein-Uhlenbeck process is studied in this paper. We demonstrate the existence and uniqueness of the positive solution by constructing the Lyapunov function. The adequate conditions for the solution's stationary distribution were described. Last but not least, the numerical simulation demonstrated that reversion rates and noise intensity influenced the disease and that there was a stationary distribution. It was concluded that the solution tends more toward the stationary distribution, the greater the reversion rates and the smaller the noise.
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Affiliation(s)
- Zhenyu Zhang
- Academy of Fine Arts, Xinxiang University, Xinxiang, P.R. China
| | - Guizhen Liang
- School of Mathematics and Statistics, Xinxiang University, Xinxiang, P.R. China
| | - Kangkang Chang
- School of Mathematics and Statistics, Xinxiang University, Xinxiang, P.R. China
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4
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Phan T, Brozak S, Pell B, Oghuan J, Gitter A, Hu T, Ribeiro RM, Ke R, Mena KD, Perelson AS, Kuang Y, Wu F. Making waves: Integrating wastewater surveillance with dynamic modeling to track and predict viral outbreaks. WATER RESEARCH 2023; 243:120372. [PMID: 37494742 DOI: 10.1016/j.watres.2023.120372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2023] [Revised: 07/10/2023] [Accepted: 07/15/2023] [Indexed: 07/28/2023]
Abstract
Wastewater surveillance has proved to be a valuable tool to track the COVID-19 pandemic. However, most studies using wastewater surveillance data revolve around establishing correlations and lead time relative to reported case data. In this perspective, we advocate for the integration of wastewater surveillance data with dynamic within-host and between-host models to better understand, monitor, and predict viral disease outbreaks. Dynamic models overcome emblematic difficulties of using wastewater surveillance data such as establishing the temporal viral shedding profile. Complementarily, wastewater surveillance data bypasses the issues of time lag and underreporting in clinical case report data, thus enhancing the utility and applicability of dynamic models. The integration of wastewater surveillance data with dynamic models can enhance real-time tracking and prevalence estimation, forecast viral transmission and intervention effectiveness, and most importantly, provide a mechanistic understanding of infectious disease dynamics and the driving factors. Dynamic modeling of wastewater surveillance data will advance the development of a predictive and responsive monitoring system to improve pandemic preparedness and population health.
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Affiliation(s)
- Tin Phan
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Samantha Brozak
- School of Mathematical and Statistical Sciences, Arizona State University, AZ 85281, USA
| | - Bruce Pell
- Department of Mathematics and Computer Science, Lawrence Technological University, MI 48075, USA
| | - Jeremiah Oghuan
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
| | - Anna Gitter
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
| | - Tao Hu
- Department of Geography, Oklahoma State University, Stillwater, OK 74078, USA
| | - Ruy M Ribeiro
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Ruian Ke
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Kristina D Mena
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA; Texas Epidemic Public Health Institute, Houston, TX 77030, USA
| | - Alan S Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA; Santa Fe Institute, Santa Fe, NM 87501, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, AZ 85281, USA
| | - Fuqing Wu
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA; Texas Epidemic Public Health Institute, Houston, TX 77030, USA.
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5
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El Messaoudi S, Lemenuel-Diot A, Gonçalves A, Guedj J. A Semi-mechanistic Model to Characterize the Long-Term Dynamics of Hepatitis B Virus Markers During Treatment With Lamivudine and Pegylated Interferon. Clin Pharmacol Ther 2023; 113:390-400. [PMID: 36408671 DOI: 10.1002/cpt.2798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 11/07/2022] [Indexed: 11/22/2022]
Abstract
Antiviral treatments against hepatitis B virus (HBV) suppress viral replication but do not eradicate the virus, and need therefore to be taken lifelong to avoid relapse. Mathematical models can be useful to support the development of curative anti-HBV agents; however, they mostly focus on short-term HBV DNA data and neglect the complex host-pathogen interaction. This work aimed to characterize the effect of treatment with lamivudine and/or pegylated interferon (Peg-IFN) in 1,300 patients (hepatitis B envelope antigen (HBeAg)-positive and HBeAg-negative) treated for 1 year. A mathematical model was developed incorporating two populations of infected cells, namely I 1 , with a high transcriptional activity, that progressively evolve into I 2 , at a rate δ tr , representing cells with integrated HBV DNA that have a lower transcriptional activity. Parameters of the model were estimated in patients treated with lamivudine or Peg-IFN alone (N = 894), and the model was then validated in patients treated with lamivudine plus Peg-IFN (N = 436) to predict the virological response after a year of combination treatment. Lamivudine had a larger effect in blocking viral production than Peg-IFN (99.4-99.9% vs. 91.8-95.1%); however, Peg-IFN had a significant immunomodulatory effect, leading to an enhancement of the loss rates of I 1 (×1.7 in HBeAg-positive patients), I 2 (> ×7 irrespective of HBeAg status), and δ tr (×4.6 and ×2.0 in HBeAg-positive and HBeAg-negative patients, respectively). Using this model, we were able to describe the synergy of the different effects occurring during treatment with combination and predicted an effect of 99.99% on blocking viral production. This framework can therefore support the optimization of combination therapy with new anti-HBV agents.
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Affiliation(s)
- Selma El Messaoudi
- Université Paris Cité, Institut National de la Santé et de la Recherche Médicale, Infection, Antimicrobials, Modelling, Evolution, Paris, France
| | - Annabelle Lemenuel-Diot
- Pharmaceutical Sciences, Roche Pharmaceutical Research and Early Development, Roche Innovation Center, Basel, Switzerland
| | - Antonio Gonçalves
- Université Paris Cité, Institut National de la Santé et de la Recherche Médicale, Infection, Antimicrobials, Modelling, Evolution, Paris, France
| | - Jérémie Guedj
- Université Paris Cité, Institut National de la Santé et de la Recherche Médicale, Infection, Antimicrobials, Modelling, Evolution, Paris, France
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6
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Huang R, Chen J, Tan Q, Hu W, Chen X, Yu Y, Zang G, Tang Z. Role of Autophagy in the Ubiquitinated Hepatitis B Virus Core Antigen Enhancing Dendritic Cell Function. Viral Immunol 2022; 35:629-639. [DOI: 10.1089/vim.2022.0062] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Affiliation(s)
- Run Huang
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Jie Chen
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Quanhui Tan
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Weiwei Hu
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Xiaohua Chen
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Yongsheng Yu
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Guoqing Zang
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Zhenghao Tang
- Department of Infectious Disease, Shanghai Sixth People's Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China
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7
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Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2. Viruses 2022; 14:v14030605. [PMID: 35337012 PMCID: PMC8953050 DOI: 10.3390/v14030605] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Revised: 03/08/2022] [Accepted: 03/10/2022] [Indexed: 02/06/2023] Open
Abstract
We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.
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8
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Churkin A, Kriss S, Uziel A, Goyal A, Zakh R, Cotler SJ, Etzion O, Shlomai A, Rotstein HG, Dahari H, Barash D. Machine learning for mathematical models of HCV kinetics during antiviral therapy. Math Biosci 2022; 343:108756. [PMID: 34883104 PMCID: PMC8792269 DOI: 10.1016/j.mbs.2021.108756] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Revised: 11/04/2021] [Accepted: 11/04/2021] [Indexed: 01/03/2023]
Abstract
Mathematical models for hepatitis C virus (HCV) dynamics have provided a means for evaluating the antiviral effectiveness of therapy and estimating treatment outcomes such as the time to cure. Recently, a mathematical modeling approach was used in the first proof-of-concept clinical trial assessing in real-time the utility of response-guided therapy with direct-acting antivirals (DAAs) in chronic HCV-infected patients. Several retrospective studies have shown that mathematical modeling of viral kinetics predicts time to cure of less than 12 weeks in the majority of individuals treated with sofosbuvir-based as well as other DAA regimens. A database of these studies was built, and machine learning methods were evaluated for their ability to estimate the time to cure for each patient to facilitate real-time modeling studies. Data from these studies exploring mathematical modeling of HCV kinetics under DAAs in 266 chronic HCV-infected patients were gathered. Different learning methods were applied and trained on part of the dataset ('train' set), to predict time to cure on the untrained part ('test' set). Our results show that this machine learning approach provides a means for establishing an accurate time to cure prediction that will support the implementation of individualized treatment.
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Affiliation(s)
- Alexander Churkin
- Department of Software Engineering, Sami Shamoon College of Engineering, Beer-Sheba, Israel
| | - Stephanie Kriss
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Asher Uziel
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Ashish Goyal
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Rami Zakh
- Department of Computer Science, Ben-Gurion University, Israel
| | - Scott J Cotler
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA
| | - Ohad Etzion
- Soroka University Medical Center, Beer-Sheba, Israel
| | - Amir Shlomai
- Department of Medicine D and The Liver Institute, Rabin Medical Center, Beilinson Hospital, Petah-Tikva and the Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Horacio G Rotstein
- Federated Department of Biological Sciences, New Jersey Institute of Technology and Rutgers University, Newark, NJ, USA; Institute for Future Technologies, New Jersey Institute of Technology, Newark, NJ, USA
| | - Harel Dahari
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, USA.
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University, Israel.
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9
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Heitzman-Breen N, Golden J, Vazquez A, Kuchinsky SC, Duggal NK, Ciupe SM. Modeling the dynamics of Usutu virus infection in birds. J Theor Biol 2021; 531:110896. [PMID: 34506809 DOI: 10.1016/j.jtbi.2021.110896] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 08/30/2021] [Accepted: 09/02/2021] [Indexed: 02/08/2023]
Abstract
Usutu virus is an emerging zoonotic flavivirus causing high avian mortality rates and occasional severe neurological disorders in humans. Several virus strains are co-circulating and the differences in their characteristics and avian pathogenesis levels are still unknown. In this study, we use within-host mathematical models to characterize the mechanisms responsible for virus expansion and clearance in juvenile chickens challenged with four Usutu virus strains. We find heterogeneity between the virus strains, with the time between cell infection and viral production varying between 16 h and 23 h, the infected cell lifespan varying between 48 min and 9.5 h, and the basic reproductive number R0 varying between 12.05 and 19.49. The strains with high basic reproductive number have short infected cell lifespan, indicative of immune responses. The virus strains with low basic reproductive number have lower viral peaks and longer lasting viremia, due to lower infection rates and high infected cell lifespan. We discuss how the host and virus heterogeneities may differently impact the public health threat presented by these virus strains.
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Affiliation(s)
- Nora Heitzman-Breen
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Jacob Golden
- Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Ana Vazquez
- National Centre for Microbiology, Instituto de Salud Carlos III (ISCIII), Epidemiology and Public Health Network of Biomedical Research Centre (CIBERESP), Madrid, Spain
| | - Sarah C Kuchinsky
- Department of Biomedical Sciences and Pathobiology, Virginia-Maryland College of Veterinary Medicine, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Nisha K Duggal
- Department of Biomedical Sciences and Pathobiology, Virginia-Maryland College of Veterinary Medicine, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Stanca M Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA.
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10
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Gonçalves A, Lemenuel-Diot A, Guedj J. Reply to: 'Early HBV RNA kinetics under NA treatment may reveal new insights into HBV RNA dynamics and NA mode of action'. J Viral Hepat 2021; 28:689-690. [PMID: 33462946 DOI: 10.1111/jvh.13470] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/04/2020] [Accepted: 12/14/2020] [Indexed: 12/09/2022]
Affiliation(s)
| | - Annabelle Lemenuel-Diot
- Roche Pharmaceutical Research and Early Development, Pharmaceutical Sciences, Roche Innovation Center Basel, Basel, Switzerland
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11
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Ciupe SM, Vaidya NK, Forde JE. Early events in hepatitis B infection: the role of inoculum dose. Proc Biol Sci 2021; 288:20202715. [PMID: 33563115 DOI: 10.1098/rspb.2020.2715] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The relationship between the inoculum dose and the ability of the pathogen to invade the host is poorly understood. Experimental studies in non-human primates infected with different inoculum doses of hepatitis B virus have shown a non-monotonic relationship between dose magnitude and infection outcome, with high and low doses leading to 100% liver infection and intermediate doses leading to less than 0.1% liver infection, corresponding to CD4 T-cell priming. Since hepatitis B clearance is CD8 T-cell mediated, the question of whether the inoculum dose influences CD8 T-cell dynamics arises. To help answer this question, we developed a mathematical model of virus-host interaction following hepatitis B virus infection. Our model explains the experimental data well, and predicts that the inoculum dose affects both the timing of the CD8 T-cell expansion and the quality of its response, especially the non-cytotoxic function. We find that a low-dose challenge leads to slow CD8 T-cell expansion, weak non-cytotoxic functions, and virus persistence; high- and medium-dose challenges lead to fast CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance; while a super-low-dose challenge leads to delayed CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance. These results are useful for designing immune cell-based interventions.
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Affiliation(s)
- Stanca M Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, 24060 VA, USA
| | - Naveen K Vaidya
- Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA.,Computational Science Research Center, San Diego State University, San Diego, CA 92182, USA.,Viral Information Institute, San Diego State University, San Diego, CA 92182, USA
| | - Jonathan E Forde
- Department of Mathematics and Computer Science, Hobart and William Smith Colleges, Geneva, New York 14456, USA
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12
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Kadelka S, Dahari H, Ciupe SM. Understanding the antiviral effects of RNAi-based therapy in HBeAg-positive chronic hepatitis B infection. Sci Rep 2021; 11:200. [PMID: 33420293 PMCID: PMC7794570 DOI: 10.1038/s41598-020-80594-6] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 12/21/2020] [Indexed: 01/29/2023] Open
Abstract
The RNA interference (RNAi) drug ARC-520 was shown to be effective in reducing serum hepatitis B virus (HBV) DNA, hepatitis B e antigen (HBeAg) and hepatitis B surface antigen (HBsAg) in HBeAg-positive patients treated with a single dose of ARC-520 and daily nucleosidic analogue (entecavir). To provide insights into HBV dynamics under ARC-520 treatment and its efficacy in blocking HBV DNA, HBsAg, and HBeAg production we developed a multi-compartmental pharmacokinetic-pharamacodynamic model and calibrated it with frequent measured HBV kinetic data. We showed that the time-dependent single dose ARC-520 efficacies in blocking HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% in 1-4 months. The combined single dose ARC-520 and entecavir effect on HBV DNA was constant over time, with efficacy of more than 99.8%. The observed continuous HBV DNA decline is entecavir mediated, the strong but transient HBsAg and HBeAg decays are ARC-520 mediated. The modeling framework may help assess ongoing RNAi drug development for hepatitis B virus infection.
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Affiliation(s)
- Sarah Kadelka
- Department of Mathematics, Virginia Tech, Blacksburg, VA, 24060, USA
| | - Harel Dahari
- Program for Experimental and Theoretical Modeling, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, 60153, USA
| | - Stanca M Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA, 24060, USA.
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13
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Leveraging Computational Modeling to Understand Infectious Diseases. CURRENT PATHOBIOLOGY REPORTS 2020; 8:149-161. [PMID: 32989410 PMCID: PMC7511257 DOI: 10.1007/s40139-020-00213-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Accepted: 09/16/2020] [Indexed: 02/06/2023]
Abstract
Purpose of Review Computational and mathematical modeling have become a critical part of understanding in-host infectious disease dynamics and predicting effective treatments. In this review, we discuss recent findings pertaining to the biological mechanisms underlying infectious diseases, including etiology, pathogenesis, and the cellular interactions with infectious agents. We present advances in modeling techniques that have led to fundamental disease discoveries and impacted clinical translation. Recent Findings Combining mechanistic models and machine learning algorithms has led to improvements in the treatment of Shigella and tuberculosis through the development of novel compounds. Modeling of the epidemic dynamics of malaria at the within-host and between-host level has afforded the development of more effective vaccination and antimalarial therapies. Similarly, in-host and host-host models have supported the development of new HIV treatment modalities and an improved understanding of the immune involvement in influenza. In addition, large-scale transmission models of SARS-CoV-2 have furthered the understanding of coronavirus disease and allowed for rapid policy implementations on travel restrictions and contract tracing apps. Summary Computational modeling is now more than ever at the forefront of infectious disease research due to the COVID-19 pandemic. This review highlights how infectious diseases can be better understood by connecting scientists from medicine and molecular biology with those in computer science and applied mathematics.
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14
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Churkin A, Lewkiewicz S, Reinharz V, Dahari H, Barash D. Efficient Methods for Parameter Estimation of Ordinary and Partial Differential Equation Models of Viral Hepatitis Kinetics. MATHEMATICS 2020; 8. [PMID: 33224865 PMCID: PMC7676746 DOI: 10.3390/math8091483] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Parameter estimation in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation that addresses all cases of data points available presents a formidable challenge and efficiency considerations need to be employed in order for the method to become practical. In the case of age-structured models of viral hepatitis dynamics under antiviral treatment that deal with partial differential equations, a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derivative approximations. The newly efficient methods that were developed as a result of the above approach are described for hepatitis C virus kinetic models during antiviral therapy. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for both the ordinary and partial differential equation models.
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Affiliation(s)
- Alexander Churkin
- Department of Software Engineering, Sami Shamoon College of Engineering, Beer-Sheva 8410501, Israel
- Correspondence: (A.C.); (D.B.); Tel.: +972-8-647-5281 (A.C.); +972-8-647-2714 (D.B.)
| | - Stephanie Lewkiewicz
- Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095, USA
| | - Vladimir Reinharz
- Department of Computer Science, Université du Québec à Montréal, Montreal, QC H3C 3P8, Canada
| | - Harel Dahari
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Medical Center, Maywoood, IL 60153, USA
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University, Beer-Sheva 8410501, Israel
- Correspondence: (A.C.); (D.B.); Tel.: +972-8-647-5281 (A.C.); +972-8-647-2714 (D.B.)
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15
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Tang R, Lei Z, Wang X, Qi Q, He J, Liu D, Wang X, Chen X, Zhu J, Li Y, Zhou S, Su C. Hepatitis B envelope antigen increases Tregs by converting CD4+CD25 - T cells into CD4 +CD25 +Foxp3 + Tregs. Exp Ther Med 2020; 20:3679-3686. [PMID: 32855720 PMCID: PMC7444405 DOI: 10.3892/etm.2020.9107] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 07/01/2020] [Indexed: 12/14/2022] Open
Abstract
Hepatitis B virus (HBV) can establish a lifelong chronic infection in humans, leading to liver cirrhosis, liver failure and hepatocellular carcinoma. Patients with chronic hepatitis B (CHB) exhibit a weak virus-specific immune response. Regulatory T cells (Tregs) play a key role in regulating the immune response in patients with CHB. Patients with hepatitis B envelope antigen (HBeAg)-positive CHB harbored a higher percentage of Tregs in their peripheral blood than those with HBeAg-negative CHB. However, whether and how HBeAg manipulates the host immune system to increase the population of Tregs remains to be elucidated. The present manuscript describes a preliminary immunological study of HBeAg in a mouse model. Multiple potential CD4+ T cell epitopes in HBeAg were identified using Immune Epitope Database consensus binding prediction. It was demonstrated that HBeAg treatment increased the numbers of Tregs in mouse spleens in vitro and in vivo. Furthermore, it was indicated that the HBeAg-mediated increase in Tregs occurred through the conversion of CD4+CD25- T cells into CD4+CD25+Foxp3+ Tregs. Additionally, in vitro study illustrated that HBeAg stimulated murine spleen cells to produce increased transforming growth factor-β, which is required to enable HBeAg to convert T cells into Tregs. The results of the present study may provide further evidence of the effect of HBeAg on Tregs and aid in the development of novel HBeAg-based immunotherapy for CHB.
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Affiliation(s)
- Rui Tang
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Zhigang Lei
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Xinpeng Wang
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Qianqian Qi
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Jingjing He
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Dan Liu
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Xiaoxian Wang
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Xiaojun Chen
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Jifeng Zhu
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Yalin Li
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Sha Zhou
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
| | - Chuan Su
- State Key Laboratory of Reproductive Medicine, Department of Pathogen Biology and Immunology, Jiangsu Key Laboratory of Pathogen Biology, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, P.R. China
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Gonçalves A, Mentré F, Lemenuel-Diot A, Guedj J. Model Averaging in Viral Dynamic Models. AAPS JOURNAL 2020; 22:48. [PMID: 32060662 DOI: 10.1208/s12248-020-0426-7] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2019] [Accepted: 01/16/2020] [Indexed: 12/24/2022]
Abstract
The paucity of experimental data makes both inference and prediction particularly challenging in viral dynamic models. In the presence of several candidate models, a common strategy is model selection (MS), in which models are fitted to the data but only results obtained with the "best model" are presented. However, this approach ignores model uncertainty, which may lead to inaccurate predictions. When several models provide a good fit to the data, another approach is model averaging (MA) that weights the predictions of each model according to its consistency to the data. Here, we evaluated by simulations in a nonlinear mixed-effect model framework the performances of MS and MA in two realistic cases of acute viral infection, i.e., (1) inference in the presence of poorly identifiable parameters, namely, initial viral inoculum and eclipse phase duration, (2) uncertainty on the mechanisms of action of the immune response. MS was associated in some scenarios with a large rate of false selection. This led to a coverage rate lower than the nominal coverage rate of 0.95 in the majority of cases and below 0.50 in some scenarios. In contrast, MA provided better estimation of parameter uncertainty, with coverage rates ranging from 0.72 to 0.98 and mostly comprised within the nominal coverage rate. Finally, MA provided similar predictions than those obtained with MS. In conclusion, parameter estimates obtained with MS should be taken with caution, especially when several models well describe the data. In this situation, MA has better performances and could be performed to account for model uncertainty.
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Affiliation(s)
- Antonio Gonçalves
- Université de Paris, IAME, INSERM, Henri Huchard, F-75018, Paris, France.
| | - France Mentré
- Université de Paris, IAME, INSERM, Henri Huchard, F-75018, Paris, France
| | - Annabelle Lemenuel-Diot
- Roche Pharmaceutical Research and Early Development, Pharmaceutical Sciences, Roche Innovation Center, Basel, Switzerland
| | - Jérémie Guedj
- Université de Paris, IAME, INSERM, Henri Huchard, F-75018, Paris, France
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Survivin expression starts before hepatocellular cancer development in the liver of chronic hepatitis B patients: a pilot, cross-sectional study. GASTROENTEROLOGY REVIEW 2019; 15:138-143. [PMID: 32550946 PMCID: PMC7294976 DOI: 10.5114/pg.2019.87081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Accepted: 07/15/2019] [Indexed: 11/17/2022]
Abstract
Introduction Survivin expression is well known feature of hepatocellular carcinoma (HCC); however, there is no information about survivin expression in chronic hepatitis B (CHB). Aim Investigating survivin expression in the liver of CHB patients. Material and methods This is a single-centre, cross-sectional study. Seventy-five CHB patients and eight control patients were enrolled into the study between 2008 and 2018. Immunohistochemical study was performed by using anti-survivin antibody to evaluate survivin immunoreactivity. Results Survivin immunoreactivity was significantly higher in CHB patients compared to controls (p = 0.008). Also, the degree of survivin immunoreactivity was significantly higher in CHB patients (p = 0.027). Between the anti-survivin-positive and anti-survivin-negative groups, baseline laboratory parameters and initial pathology features were not significantly different. Conclusions This is the first study evaluating survivin expression in CHB patients. Understanding the possible relationship between survivin expression and HCC development in this population can promote new studies in terms of new therapies and treatment timing.
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Abstract
Viruses are a main cause of disease worldwide and many are without effective therapeutics or vaccines. A lack of understanding about how host responses work to control viral spread is one factor limiting effective management. How different immune components regulate infection dynamics is beginning to be better understood with the help of mathematical models. These models have been key in discriminating between hypotheses and in identifying rates of virus growth and clearance, dynamical control by different host factors and antivirals, and synergistic interactions during multi-pathogen infections. A recent focus in evaluating model predictions in the laboratory and clinic has illuminate the accuracy of models for a variety of viruses and highlighted the critical nature of theoretical approaches in virology. Here, I discuss recent model-driven exploration of host-pathogen interactions that have illustrated the importance of model validation in establishing the model's predictive capability and in defining new biology.
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19
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Chen C, Liu Y, Wang H, Chen G, Wu X, Ren J, Zhang H, Zhao Y. Multifunctional Chitosan Inverse Opal Particles for Wound Healing. ACS NANO 2018; 12:10493-10500. [PMID: 30256608 DOI: 10.1021/acsnano.8b06237] [Citation(s) in RCA: 94] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Wound healing is one of the most important and basic issues faced by the medical community. In this paper, we present biomass-composited inverse opal particles with a series of advanced features for drug delivery and wound healing. The particles were derived by using chitosan biomass to negatively replicate spherical colloid crystal templates. Because of the interconnected porous structures, various forms of active drugs, including fibroblast growth factor could be loaded into the void spaces of the inverse opal particles and encapsulated by temperature-responsive hydrogel. This endowed the composited particles with the capability of intelligent drug release through the relatively high temperature caused by the inflammation reaction at wound sites. Because the structural colors and characteristic reflection peaks of the composited inverse opal particles are blue-shifted during the release process, the drug delivery can be monitored in real time. It was demonstrated that the biomass-composited microcarriers were able to promote angiogenesis, collagen deposition, and granulation-tissue formation as well as reduce inflammation and thus significantly contributed to wound healing. These features point to the potential value of multifunctional biomass inverse opal particles in biomedicine.
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Affiliation(s)
- Canwen Chen
- Department of General Surgery, Jinling Hospital , Medical School of Nanjing University , Nanjing 210002 , China
| | - Yuxiao Liu
- State Key Laboratory of Bioelectronics, School of Biological Science and Medical Engineering , Southeast University , Nanjing 210096 , China
| | - Huan Wang
- State Key Laboratory of Bioelectronics, School of Biological Science and Medical Engineering , Southeast University , Nanjing 210096 , China
| | - Guopu Chen
- Department of General Surgery, Jinling Hospital , Medical School of Nanjing University , Nanjing 210002 , China
| | - Xiuwen Wu
- Department of General Surgery, Jinling Hospital , Medical School of Nanjing University , Nanjing 210002 , China
| | - Jianan Ren
- Department of General Surgery, Jinling Hospital , Medical School of Nanjing University , Nanjing 210002 , China
| | - Huidan Zhang
- School of Engineering and Applied Sciences and Department of Physics , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Yuanjin Zhao
- Department of General Surgery, Jinling Hospital , Medical School of Nanjing University , Nanjing 210002 , China
- State Key Laboratory of Bioelectronics, School of Biological Science and Medical Engineering , Southeast University , Nanjing 210096 , China
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20
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Affiliation(s)
- Alan S Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Ruy M Ribeiro
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, USA
- Laboratorio de Biomatematica, Faculdade de Medicina da Universidade de Lisboa, Lisboa, Portugal
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