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Raezah AA, Elaiw A, Alshaikh M. Global stability of secondary DENV infection models with non-specific and strain-specific CTLs. Heliyon 2024; 10:e25391. [PMID: 38352732 PMCID: PMC10862684 DOI: 10.1016/j.heliyon.2024.e25391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Revised: 12/30/2023] [Accepted: 01/25/2024] [Indexed: 02/16/2024] Open
Abstract
Dengue virus (DENV) is a highly perilous virus that is transmitted to humans through mosquito bites and causes dengue fever. Consequently, extensive efforts are being made to develop effective treatments and vaccines. Mathematical modeling plays a significant role in comprehending the dynamics of DENV within a host in the presence of cytotoxic T lymphocytes (CTL) immune response. This study examines two models for secondary DENV infections that elucidate the dynamics of DENV under the influence of two types of CTL responses, namely non-specific and strain-specific responses. The first model encompasses five compartments, which consist of uninfected monocytes, infected monocytes, free DENV particles, non-specific CTLs, and strain-specific CTLs. In the second model, latently infected cells are introduced into the model. We posit that the CTL responsiveness is determined by a combination of self-regulating CTL response and a predator-prey-like CTL response. The model's solutions are verified to be nonnegativity and bounded and the model possesses two equilibrium states: the uninfected equilibrium EQ 0 and the infected equilibrium EQ ⁎ . Furthermore, we calculate the basic reproduction number R 0 , which determines the existence and stability of the model's equilibria. We examine the global stability by constructing suitable Lyapunov functions. Our analysis reveals that if R 0 ≤ 1 , then EQ 0 is globally asymptotically stable (G.A.S), and if R 0 > 1 , then EQ 0 is unstable while EQ ⁎ is G.A.S. To illustrate our findings analytically, we conduct numerical simulations for each model. Additionally, we perform sensitivity analysis to demonstrate how the parameter values of the proposed model impact R 0 given a set of data. Finally, we discuss the implications of including the CTL immune response and latently infected cells in the secondary DENV infection model. Our study demonstrates that incorporating the CTL immune response and latently infected cells diminishes R 0 and enhances the system's stability around EQ 0 .
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Affiliation(s)
- Aeshah A. Raezah
- Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia
| | - A.M. Elaiw
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
| | - M.A. Alshaikh
- Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
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Giorgakoudi K, Schley D, Juleff N, Gubbins S, Ward J. The role of Type I interferons in the pathogenesis of foot-and-mouth disease virus in cattle: A mathematical modelling analysis. Math Biosci 2023; 363:109052. [PMID: 37495013 DOI: 10.1016/j.mbs.2023.109052] [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: 01/27/2023] [Revised: 06/16/2023] [Accepted: 07/18/2023] [Indexed: 07/28/2023]
Abstract
Type I interferons (IFN) are the first line of immune response against infection. In this study, we explore the interaction between Type I IFN and foot-and-mouth disease virus (FMDV), focusing on the effect of this interaction on epithelial cell death. While several mathematical models have explored the interaction between interferon and viruses at a systemic level, with most of the work undertaken on influenza and hepatitis C, these cannot investigate why a virus such as FMDV causes extensive cell death in some epithelial tissues leading to the development of lesions, while other infected epithelial tissues exhibit negligible cell death. Our study shows how a model that includes epithelial tissue structure can explain the development of lesions in some tissues and their absence in others. Furthermore, we show how the site of viral entry in an epithelial tissue, the viral replication rate, IFN production, suppression of viral replication by IFN and IFN release by live cells, all have a major impact on results.
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Affiliation(s)
- Kyriaki Giorgakoudi
- The Pirbright Institute, Ash Road, Pirbright, Surrey, GU24 0NF, UK; Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK.
| | - David Schley
- The Pirbright Institute, Ash Road, Pirbright, Surrey, GU24 0NF, UK.
| | - Nicholas Juleff
- The Pirbright Institute, Ash Road, Pirbright, Surrey, GU24 0NF, UK.
| | - Simon Gubbins
- The Pirbright Institute, Ash Road, Pirbright, Surrey, GU24 0NF, UK.
| | - John Ward
- Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK.
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Rana P, Chauhan S, Mubayi A. Burden of cytokines storm on prognosis of SARS-CoV-2 infection through immune response: dynamic analysis and optimal control with immunomodulatory therapy. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:3297-3315. [PMID: 35103099 PMCID: PMC8792534 DOI: 10.1140/epjs/s11734-022-00435-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Accepted: 12/20/2021] [Indexed: 06/14/2023]
Abstract
Immune responses have a crucial role to play against SARS-CoV-2 virus as the adaptive and innate immune systems of the human body help restoring the body to a healthy stage by annihilating this deadly viral infection. Cytokines also play a significant role in modulating a balance between innate and adaptive immune responses but excess of it can have a detrimental affect on critically ill patients. Therefore, this paper is a novel attempt to formulate a within-host mathematical model showing the impact of cytokines storm on healthy cells. The dynamics of the system is analysed which involves basic reproduction number, steady state solutions and global dynamics for disease-free point and endemic equilibrium using geometric approach. Further, an optimal control problem is discussed considering immunomodulatory therapy (targeting cytokines signaling) as control using linear feedback control method to increase the level of healthy cells, which provides vitality for our system. Through numerical simulations, analytic solutions are validated followed by the curve-fit for the cytokines using real data and an optimization algorithm for optimal fit. Finally, sensitivity analysis for the basic reproduction number and the rate of change of healthy cells using Latin Hypercube Sampling method (LHS) is performed. Our finding suggests that immunomodulatory therapy (tocilizumab) can act as a key component to control cytokines storm for critically ill patients to restore the body to a healthy state.
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Affiliation(s)
- Payal Rana
- Department of Mathematics, Amity Institute of Applied Science, Amity University, Sector-125, Noida, UP India
| | - Sudipa Chauhan
- Department of Mathematics, Amity Institute of Applied Science, Amity University, Sector-125, Noida, UP India
| | - Anuj Mubayi
- PRECISIONheor, Los Angeles, CA USA
- Department of Mathematics, Illinois State University, Normal, IL USA
- College of Health Solutions, Arizona State University, Tempe, AZ USA
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Wang H, Tian X. Dynamics of a delayed within host model for dengue infection with immune response and Beddington–DeAngelis incidence. INT J BIOMATH 2021. [DOI: 10.1142/s1793524522500024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, a new delayed within host model for dengue fever with immune response and Beddington–DeAngelis incidence is investigated. The basic reproduction number is computed. In addition, a detailed analysis on the local and global dynamics of the model is conducted. Finally, sensitivity analysis is carried out on basic reproduction number and numerical simulations are given to elucidate our theoretical results.
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Affiliation(s)
- Haifeng Wang
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, P. R. China
| | - Xiaohong Tian
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, P. R. China
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Within Host Dynamics of SARS-CoV-2 in Humans: Modeling Immune Responses and Antiviral Treatments. SN COMPUTER SCIENCE 2021; 2:482. [PMID: 34661166 PMCID: PMC8506088 DOI: 10.1007/s42979-021-00919-8] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 10/02/2021] [Indexed: 01/04/2023]
Abstract
In December 2019, a newly discovered SARS-CoV-2 virus was emerged from China and propagated worldwide as a pandemic, resulting in about 3–5% mortality. Mathematical models can provide useful scientific insights about transmission patterns and targets for drug development. In this study, we propose a within-host mathematical model of SARS-CoV-2 infection considering innate and adaptive immune responses. We analyze the equilibrium points of the proposed model and obtain an expression of the basic reproduction number. We then numerically show the existence of a transcritical bifurcation. The proposed model is calibrated to real viral load data of two COVID-19 patients. Using the estimated parameters, we perform global sensitivity analysis with respect to the peak of viral load. Finally, we study the efficacy of antiviral drugs and vaccination on the dynamics of SARS-CoV-2 infection. Results suggest that blocking the virus production from infected cells can be an effective target for antiviral drug development. Finally, it is found that vaccination is more effective intervention as compared to the antiviral treatments.
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Nguyen HD, Chaudhury S, Waickman AT, Friberg H, Currier JR, Wallqvist A. Stochastic Model of the Adaptive Immune Response Predicts Disease Severity and Captures Enhanced Cross-Reactivity in Natural Dengue Infections. Front Immunol 2021; 12:696755. [PMID: 34484195 PMCID: PMC8416063 DOI: 10.3389/fimmu.2021.696755] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2021] [Accepted: 07/26/2021] [Indexed: 11/13/2022] Open
Abstract
The dengue virus circulates as four distinct serotypes, where a single serotype infection is typically asymptomatic and leads to acquired immunity against that serotype. However, the developed immunity to one serotype is thought to underlie the severe manifestation of the disease observed in subsequent infections from a different serotype. We developed a stochastic model of the adaptive immune response to dengue infections. We first delineated the mechanisms initiating and sustaining adaptive immune responses during primary infections. We then contrasted these immune responses during secondary infections of either a homotypic or heterotypic serotype to understand the role of pre-existing and reactivated immune pathways on disease severity. Comparison of non-symptomatic and severe cases from heterotypic infections demonstrated that overproduction of specific antibodies during primary infection induces an enhanced population of cross-reactive antibodies during secondary infection, ultimately leading to severe disease manifestations. In addition, the level of disease severity was found to correlate with immune response kinetics, which was dependent on beginning lymphocyte levels. Our results detail the contribution of specific lymphocytes and antibodies to immunity and memory recall that lead to either protective or pathological outcomes, allowing for the understanding and determination of mechanisms of protective immunity.
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Affiliation(s)
- Hung D Nguyen
- Biotechnology High Performance Computing (HPC) Software Applications Institute, Telemedicine and Advanced Technology Research Center, U.S. Army Medical Research and Development Command, Fort Detrick, MD, United States.,Henry M. Jackson Foundation for the Advancement of Military Medicine, Bethesda, MD, United States
| | - Sidhartha Chaudhury
- Center for Enabling Capabilities, Walter Reed Army Institute of Research, Silver Spring, MD, United States
| | - Adam T Waickman
- Department of Microbiology and Immunology, State University of New York Upstate Medical University, Syracuse, NY, United States
| | - Heather Friberg
- Viral Diseases Branch, Walter Reed Army Institute of Research, Silver Spring, MD, United States
| | - Jeffrey R Currier
- Viral Diseases Branch, Walter Reed Army Institute of Research, Silver Spring, MD, United States
| | - Anders Wallqvist
- Biotechnology High Performance Computing (HPC) Software Applications Institute, Telemedicine and Advanced Technology Research Center, U.S. Army Medical Research and Development Command, Fort Detrick, MD, United States
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de A Camargo F, Adimy M, Esteva L, Métayer C, Ferreira CP. Modeling the Relationship Between Antibody-Dependent Enhancement and Disease Severity in Secondary Dengue Infection. Bull Math Biol 2021; 83:85. [PMID: 34142264 DOI: 10.1007/s11538-021-00919-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 06/05/2021] [Indexed: 11/25/2022]
Abstract
Sequential infections with different dengue serotypes (DENV-1, 4) significantly increase the risk of a severe disease outcome (fever, shock, and hemorrhagic disorders). Two hypotheses have been proposed to explain the severity of the disease: (1) antibody-dependent enhancement (ADE) and (2) original T cell antigenic sin. In this work, we explored the first hypothesis through mathematical modeling. The proposed model reproduces the dynamic of susceptible and infected target cells and dengue virus in scenarios of infection-neutralizing and infection-enhancing antibody competition induced by two distinct serotypes of the dengue virus during secondary infection. The enhancement and neutralization functions are derived from basic concepts of chemical reactions and used to mimic binding to the virus by two distinct populations of antibodies. The analytic study of the model showed the existence of two equilibriums: a disease-free equilibrium and an endemic one. Using the concept of the basic reproduction number [Formula: see text], we performed the asymptotic stability analysis for the two equilibriums. To measure the severity of the disease, we considered the maximum value of infected cells as well as the time when this maximum is reached. We observed that it corresponds to the time when the maximum enhancing activity for the infection occurs. This critical time was calculated from the model to be a few days after the occurrence of the infection, which corresponds to what is observed in the literature. Finally, using as output [Formula: see text], we were able to rank the contribution of each parameter of the model. In particular, we highlighted that the cross-reactive antibody responses may be responsible for the disease enhancement during secondary heterologous dengue infection.
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Affiliation(s)
- Felipe de A Camargo
- Institute of Biosciences, São Paulo State University (UNESP), Botucatu, SP, 18618-689, Brazil
| | - Mostafa Adimy
- Inria, Institut Camille Jordan, Université de Lyon, Université Lyon 1, 43 Bd. du 11 novembre 1918, 69200, Villeurbanne Cedex, France
| | - Lourdes Esteva
- Departamento de Matemáticas, Facultad de Ciencias, UNAM, 04510, Mexico, D.F., Mexico
| | - Clémence Métayer
- Inria, Institut Camille Jordan, Université de Lyon, Université Lyon 1, 43 Bd. du 11 novembre 1918, 69200, Villeurbanne Cedex, France
| | - Cláudia P Ferreira
- Institute of Biosciences, São Paulo State University (UNESP), Botucatu, SP, 18618-689, Brazil.
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Kim HO, Na W, Yeom M, Lim JW, Bae EH, Park G, Park C, Lee H, Kim HK, Jeong DG, Lyoo KS, Le VP, Haam S, Song D. Dengue Virus-Polymersome Hybrid Nanovesicles for Advanced Drug Screening Using Real-Time Single Nanoparticle-Virus Tracking. ACS APPLIED MATERIALS & INTERFACES 2020; 12:6876-6884. [PMID: 31950828 DOI: 10.1021/acsami.9b20492] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Dengue virus (DENV) is a major infectious viral pathogen that affects millions of individuals worldwide every year, causing a potentially fatal syndrome, while no commercial antiviral drugs are yet available. To develop an antiviral against dengue fever, it is necessary to understand the relationship between DENV and host cells, which could provide a basis for viral dynamics and identification of inhibitory drug targets. In this study, we designed DiD-loaded and BODIPY-ceramide-encapsulated DENV-polymersome hybrid nanovesicles (DENVSomes) prepared by an extrusion method, which trigger red fluorescence in the endosome and green in the Golgi. DENVSome monitors the dynamics of host cell-virus interaction and tracking in living cells with novel state-of-the-art imaging technologies that show images at high resolution. Also, DENVSome can be exploited to screen whether candidate antiviral drugs interact with DENVs. Consequently, we successfully demonstrated that DENVSome is an efficient tool for tracking and unraveling the mechanisms of replication and drug screening for antiviral drugs of DENV.
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Affiliation(s)
- Hyun-Ouk Kim
- Department of Pharmacy, College of Pharmacy , Korea University , Sejong 30019 , Republic of Korea
| | - Woonsung Na
- College of Veterinary Medicine , Chonnam National University , Gwangju 61186 , Republic of Korea
| | - Minjoo Yeom
- Department of Pharmacy, College of Pharmacy , Korea University , Sejong 30019 , Republic of Korea
| | - Jong-Woo Lim
- Department of Chemical & Biomolecular Engineering , Yonsei University , Seoul 03722 , Republic of Korea
| | - Eun-Hye Bae
- Department of Pharmacy, College of Pharmacy , Korea University , Sejong 30019 , Republic of Korea
| | - Geunseon Park
- Department of Chemical & Biomolecular Engineering , Yonsei University , Seoul 03722 , Republic of Korea
| | - Chaewon Park
- Department of Chemical & Biomolecular Engineering , Yonsei University , Seoul 03722 , Republic of Korea
| | - Hwunjae Lee
- Department of Radiology, College of Medicine , Yonsei University , Seoul 03722 , Republic of Korea
- YUHS-KRIBB Medical Convergence Research Institute , Seoul 03722 , Republic of Korea
| | - Hye Kwon Kim
- Department of Microbiology, College of Natural Sciences , Chungbuk National University , Cheongju 28644 , Republic of Korea
| | - Dae Gwin Jeong
- Infectious Disease Research Center , Korea Research Institute of Bioscience and Biotechnology , Daejeon 34141 , Republic of Korea
| | - Kwang-Soo Lyoo
- Korea Zoonosis Research Institute , Chonbuk National University , Iksan 54531 , Republic of Korea
| | - Van Phan Le
- Department of Microbiology and Infectious Diseases, College of Veterinary Medicine , Vietnam National University of Agriculture , Hanoi 100000 , Vietnam
| | - Seungjoo Haam
- Department of Chemical & Biomolecular Engineering , Yonsei University , Seoul 03722 , Republic of Korea
| | - Daesub Song
- Department of Pharmacy, College of Pharmacy , Korea University , Sejong 30019 , Republic of Korea
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Adimy M, Mancera PFA, Rodrigues DS, Santos FLP, Ferreira CP. Maternal Passive Immunity and Dengue Hemorrhagic Fever in Infants. Bull Math Biol 2020; 82:24. [DOI: 10.1007/s11538-020-00699-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2019] [Accepted: 01/10/2020] [Indexed: 12/28/2022]
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Sasmal SK, Takeuchi Y, Nakaoka S. T-Cell mediated adaptive immunity and antibody-dependent enhancement in secondary dengue infection. J Theor Biol 2019; 470:50-63. [DOI: 10.1016/j.jtbi.2019.03.010] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2018] [Revised: 02/13/2019] [Accepted: 03/12/2019] [Indexed: 11/26/2022]
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