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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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Aguiar M, Anam V, Blyuss KB, Estadilla CDS, Guerrero BV, Knopoff D, Kooi BW, Srivastav AK, Steindorf V, Stollenwerk N. Mathematical models for dengue fever epidemiology: A 10-year systematic review. Phys Life Rev 2022; 40:65-92. [PMID: 35219611 PMCID: PMC8845267 DOI: 10.1016/j.plrev.2022.02.001] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 02/08/2022] [Indexed: 01/11/2023]
Abstract
Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.
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Affiliation(s)
- Maíra Aguiar
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, Trento, 38123, Italy; Ikerbasque, Basque Foundation for Science, Bilbao, Spain.
| | - Vizda Anam
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Konstantin B Blyuss
- VU University, Faculty of Science, De Boelelaan 1085, NL 1081, HV Amsterdam, the Netherlands
| | - Carlo Delfin S Estadilla
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Bruno V Guerrero
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Damián Knopoff
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Centro de Investigaciones y Estudios de Matemática CIEM, CONICET, Medina Allende s/n, Córdoba, 5000, Argentina
| | - Bob W Kooi
- University of Sussex, Department of Mathematics, Falmer, Brighton, UK
| | - Akhil Kumar Srivastav
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Vanessa Steindorf
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain
| | - Nico Stollenwerk
- Basque Center for Applied Mathematics, Alameda de Mazarredo 14, Bilbao, E-48009, Basque Country, Spain; Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, Povo, Trento, 38123, Italy
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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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