Examining HIV progression mechanisms via mathematical approaches

The progression of HIV infection to AIDS is unclear and under examined. Many mechanisms have been proposed, including a decline in immune response, increase in replication rate, involution of the thymus, syncytium inducing capacity, activation of the latently infected cell pool, chronic activation of the immune system, and the ability of the virus to infect other immune system cells. The significance of each mechanism in combination has not been studied. We develop a simple HIV viral dynamics model incorporating proposed mechanisms as parameters that are allowed to vary. In the entire parameter space, we derive two formulae for the basic reproduction number (R0) by considering the infection starting with a single infected CD4 T cell and a single virion, respectively. We show that both formulae are equivalent. We derive analytical conditions for the occurrence of backward and forward bifurcations. To investigate the influence of the proposed mechanisms to the HIV progression, we perform uncertainty and sensitivity analysis for all parameters and conduct a bifurcation analysis on all parameters that are shown to be significant, in combination, to explore various HIV/AIDS progression dynamics.

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Lyapunov function and global asymptotic stability for a new multiscale viral dynamics model incorporating the immune system response: Implemented upon HCV

PLoS ONE ◽

10.1371/journal.pone.0257975 ◽

2021 ◽

Vol 16 (10) ◽

pp. e0257975

Author(s):

Hesham A. Elkaranshawy ◽

Hossam M. Ezzat ◽

Nermeen N. Ibrahim

Keyword(s):

Immune System ◽

Equilibrium Point ◽

Reproduction Number ◽

Initial Conditions ◽

Equilibrium Points ◽

System Response ◽

Viral Dynamics ◽

Wide Range ◽

Immune System Response

In this paper, a new mathematical model is formulated that describes the interaction between uninfected cells, infected cells, viruses, intracellular viral RNA, Cytotoxic T-lymphocytes (CTLs), and antibodies. Hence, the model contains certain biological relations that are thought to be key factors driving this interaction which allow us to obtain precise logical conclusions. Therefore, it improves our perception, that would otherwise not be possible, to comprehend the pathogenesis, to interpret clinical data, to control treatment, and to suggest new relations. This model can be used to study viral dynamics in patients for a wide range of infectious diseases like HIV, HPV, HBV, HCV, and Covid-19. Though, analysis of a new multiscale HCV model incorporating the immune system response is considered in detail, the analysis and results can be applied for all other viruses. The model utilizes a transformed multiscale model in the form of ordinary differential equations (ODE) and incorporates into it the interaction of the immune system. The role of CTLs and the role of antibody responses are investigated. The positivity of the solutions is proven, the basic reproduction number is obtained, and the equilibrium points are specified. The stability at the equilibrium points is analyzed based on the Lyapunov invariance principle. By using appropriate Lyapunov functions, the uninfected equilibrium point is proven to be globally asymptotically stable when the reproduction number is less than one and unstable otherwise. Global stability of the infected equilibrium points is considered, and it has been found that each equilibrium point has a specific domain of stability. Stability regions could be overlapped and a bistable equilibria could be found, which means the coexistence of two stable equilibrium points. Hence, the solution converges to one of them depending on the initial conditions.

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[625] NOVEL MODE OF VIRAL DECLINE DURING TELAPREVIR (VX-950) AND PEG-IFN COMBINATION TREATMENT PREDICTED BY A NEW COMBINED INTRACELLULAR AND CELLULAR HEPATITIS C VIRAL DYNAMICS MODEL

Journal of Hepatology ◽

10.1016/s0168-8278(07)62223-5 ◽

2007 ◽

Vol 46 ◽

pp. S236

Author(s):

A.U. Neumann ◽

L. Rozenberg ◽

H.W. Reesink ◽

S. Zeuzem ◽

H.M. Chu

Keyword(s):

Hepatitis C ◽

Combination Treatment ◽

Viral Dynamics ◽

Dynamics Model

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Scaling in the Immune System: PhD Thesis

10.31219/osf.io/b24kw ◽

2019 ◽

Author(s):

soumya banerjee

Keyword(s):

Immune Response ◽

Immune System ◽

Body Size ◽

Human Health ◽

Response Rates ◽

System Response ◽

Metabolic Rates ◽

Viral Dynamics ◽

Immune System Response ◽

Phd Thesis

How different is the immune system in a human from that of a mouse? Do pathogens replicate at the same rate in different species? Answers to these questions have impact on human health since multi-host pathogens that jump from animals to humans affect millions worldwide.It is not known how rates of immune response and viral dynamics vary from species to species and how they depend on species body size. Metabolic scalingtheory predicts that intracellular processes will be slower in larger animals since cellular metabolic rates are slower. We test how rates of pathogenesis and immune system response rates depend on species body size.

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De-Escalation by Reversing the Escalation with a Stronger Synergistic Package of Contact Tracing, Quarantine, Isolation and Personal Protection: Feasibility of Preventing a COVID-19 Rebound in Ontario, Canada, as a Case Study

Biology ◽

10.3390/biology9050100 ◽

2020 ◽

Vol 9 (5) ◽

pp. 100 ◽

Cited By ~ 9

Author(s):

Biao Tang ◽

Francesca Scarabel ◽

Nicola Luigi Bragazzi ◽

Zachary McCarthy ◽

Michael Glazer ◽

...

Keyword(s):

Time Series Data ◽

Necessary Conditions ◽

Reproduction Number ◽

Contact Tracing ◽

Series Data ◽

Personal Protection ◽

Dynamics Model ◽

Social Distancing ◽

Canadian Provinces

Since the beginning of the COVID-19 pandemic, most Canadian provinces have gone through four distinct phases of social distancing and enhanced testing. A transmission dynamics model fitted to the cumulative case time series data permits us to estimate the effectiveness of interventions implemented in terms of the contact rate, probability of transmission per contact, proportion of isolated contacts, and detection rate. This allows us to calculate the control reproduction number during different phases (which gradually decreased to less than one). From this, we derive the necessary conditions in terms of enhanced social distancing, personal protection, contact tracing, quarantine/isolation strength at each escalation phase for the disease control to avoid a rebound. From this, we quantify the conditions needed to prevent epidemic rebound during de-escalation by simply reversing the escalation process.

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Error catastrophe for viruses infecting cells: analysis of the phase transition in terms of error classes

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2010.0274 ◽

2010 ◽

Vol 368 (1933) ◽

pp. 5569-5582 ◽

Cited By ~ 5

Author(s):

Julia Alonso ◽

Hugo Fort

Keyword(s):

Phase Transition ◽

Rna Viruses ◽

Rna Virus ◽

Bose Condensation ◽

Viral Dynamics ◽

Replication Rate ◽

Genetic Sequence ◽

Coupled Equations ◽

Error Catastrophe ◽

Common Framework

RNA viruses offer a very exciting arena in which to study evolution in ‘real time’ owing to both their high replication rate—many generations per day are possible—and their high mutation rate, leading to a large phenotypic variety. They can be regarded as a swarm of genetically related mutants around a dominant or master genetic sequence. This system is called a ‘viral quasi-species’. Thus, a common framework to describe RNA viral dynamics is by means of the quasi-species equation (QSE). The QSE is in fact a system of a very large number of nonlinear coupled equations. Here, we consider a simpler formulation in terms of ‘error classes’, which groups all the sequences differing from the master sequence by the same number of genomic differences into one population class. From this, based on the analogies with Bose condensation, we use thermodynamic inspired observables to analyse and characterize the ‘phase transition’ through the so-called ‘RNA virus error catastrophe’.

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Chronic activation of the epithelial immune system of the fruit fly's salivary glands has a negative effect on organismal growth and induces a peculiar set of target genes

BMC Genomics ◽

10.1186/1471-2164-11-265 ◽

2010 ◽

Vol 11 (1) ◽

pp. 265 ◽

Cited By ~ 12

Author(s):

Ahmed Abdelsadik ◽

Thomas Roeder

Keyword(s):

Immune System ◽

Salivary Glands ◽

Target Genes ◽

Negative Effect ◽

Chronic Activation

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Dynamical Analysis of Multipathways and Multidelays of General Virus Dynamics Model

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419500317 ◽

2019 ◽

Vol 29 (03) ◽

pp. 1950031 ◽

Cited By ~ 6

Author(s):

Ángel G. Cervantes-Pérez ◽

Eric Ávila-Vales

Keyword(s):

Immune Response ◽

Time Delays ◽

Reproduction Number ◽

Dynamical Analysis ◽

Multiple Time Scales ◽

Threshold Dynamics ◽

Positive Equilibrium ◽

Virus Dynamics ◽

Multiple Time ◽

Dynamics Model

This paper considers a general virus dynamics model with cell-mediated immune response and direct cell-to-cell infection modes. The model incorporates two types of intracellular distributed time delays and a discrete delay in the CTL immune response. Under certain conditions, the model exhibits a global threshold dynamics with respect to two parameters: the basic reproduction number and the reproduction number of immune response. We use suitable Lyapunov functionals and apply Lasalle’s invariance principle to establish the global asymptotic stability of the two boundary equilibria. We also perform a bifurcation analysis for the positive equilibrium to show that the time delays may lead to sustained oscillations. To determine the direction of the Hopf bifurcation and the stability of the periodic solutions, the method of multiple time scales is applied. Finally, we carry out numerical simulations to illustrate our results.

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Mathematical analysis of a tuberculosis model with imperfect vaccine

International Journal of Biomathematics ◽

10.1142/s1793524519500736 ◽

2019 ◽

Vol 12 (07) ◽

pp. 1950073 ◽

Cited By ~ 1

Author(s):

A. O. Egonmwan ◽

D. Okuonghae

Keyword(s):

Reproduction Number ◽

Transmission Rate ◽

Disease Incidence ◽

Vaccination Rate ◽

Endemic Equilibrium ◽

Transmission Dynamics ◽

Treatment Rate ◽

Globally Asymptotically Stable ◽

Fast Disease Progression ◽

Latently Infected

Since 1921, the Bacille Calmette–Guerin (BCG) vaccine continues to be the most widely used vaccine for the prevention of Tuberculosis (TB). However, the immunity induced by BCG wanes out after some time making the vaccinated individual susceptible to TB infection. In this work, we formulate a mathematical model that incorporates the vaccination of newly born children and older susceptible individuals in the transmission dynamics of TB in a population, with a vaccine that can confer protection on older susceptible individuals. In the absence of disease-induced deaths, the model is shown to undergo the phenomenon of backward bifurcation where a stable disease-free equilibrium (DFE) co-exists with a stable positive (endemic) equilibrium when the associated reproduction number is less than unity. It is shown that this phenomenon does not exist in the absence of imperfect vaccine, exogenous reinfection, and reinfection of previously treated individuals. It is further shown that a special case of the model has a unique endemic equilibrium point (EEP), which is globally asymptotically stable when the associated reproduction number exceeds unity. Uncertainty and sensitivity analysis are carried out to identify key parameters that have the greatest influence on the transmission dynamics of TB in the population using the total population of latently infected individuals, total number of actively infected individuals, disease incidence, and the effective reproduction number as output responses. The analysis shows that the top five parameters of the model that have the greatest influence on the effective reproduction number of the model are the transmission rate, the fraction of fast disease progression, modification parameter which accounts for reduced likelihood to infection by vaccinated individuals due to imperfect vaccine, rate of progression from latent to active TB, and the treatment rate of actively infected individuals, with other key parameters influencing the outcomes of the other output responses. Numerical simulations suggest that with higher vaccination rate of older susceptible individuals, fewer new born children need to be vaccinated, in order to achieve disease eradication.

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Type I Interferons in Autoimmune Disease

Annual Review of Pathology Mechanisms of Disease ◽

10.1146/annurev-pathol-020117-043952 ◽

2019 ◽

Vol 14 (1) ◽

pp. 369-393 ◽

Cited By ~ 46

Author(s):

Mary K. Crow ◽

Mikhail Olferiev ◽

Kyriakos A. Kirou

Keyword(s):

Systemic Lupus Erythematosus ◽

Immune System ◽

Lupus Erythematosus ◽

Type I Interferon ◽

Type I Interferons ◽

Type I ◽

Systemic Lupus ◽

Pathway Activation ◽

Interferon Pathway ◽

Chronic Activation

Type I interferons, which make up the first cytokine family to be described and are the essential mediators of antivirus host defense, have emerged as central elements in the immunopathology of systemic autoimmune diseases, with systemic lupus erythematosus as the prototype. Lessons from investigation of interferon regulation following virus infection can be applied to lupus, with the conclusion that sustained production of type I interferon shifts nearly all components of the immune system toward pathologic functions that result in tissue damage and disease. We review recent data, mainly from studies of patients with systemic lupus erythematosus, that provide new insights into the mechanisms of induction and the immunologic consequences of chronic activation of the type I interferon pathway. Current concepts implicate endogenous nucleic acids, driving both cytosolic sensors and endosomal Toll-like receptors, in interferon pathway activation and suggest targets for development of novel therapeutics that may restore the immune system to health.

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