Semianalytical solutions by homotopy analysis method for EIAV infection with stability analysis

Geethamalini, S.; Balamuralitharan, S.

doi:10.1186/s13662-018-1808-3

Cited by 13 publications

(3 citation statements)

References 33 publications

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“…In this section, some definitions and properties of the fractional calculus and Sumudu transform are briefly mentioned. For more details see [14][15][16][17][18][19][20].…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Homotopy-Sumudu transforms for solving system of fractional partial differential equations

Alomari

2020

Adv Differ Equ

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In this paper, we investigate the Sumudu transforms and homotopy analysis method (S-HAM) for solving a system of fractional partial differential equations. A general framework for solving such a kind of problems is presented. The method can also be utilized to solve systems of fractional equations of unequal orders. The algorithm is reliable and robust. Existence and convergence results concerning the proposed solution are given. Numerical examples are introduced to demonstrate the efficiency and accuracy of the algorithm.

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“…In this section, some definitions and properties of the fractional calculus and Sumudu transform are briefly mentioned. For more details see [14][15][16][17][18][19][20].…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Homotopy-Sumudu transforms for solving system of fractional partial differential equations

Alomari

2020

Adv Differ Equ

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“…Previous modeling of EIAV analyzed virus and infected-cell dynamics with two viral strains and constant or decaying antibody levels [ 18 ], examined the protective effect of antibodies against multiple mutants [ 19 ], calculated quantitative kinetic estimates of antibody escape [ 20 ], showed that long-term dynamics depend on the ratio of cell-to-cell versus free-virus transmission [ 21 ] and calculated key kinetic parameters in the absence of adaptive immunity [ 22 ]. Other studies used EIAV as a case study to examine the mechanics of viral infection without cytopathicity [ 23 ], applied homotopy analysis to determine semi-analytical solutions [ 24 ], utilized global stability to estimate EIAV parameters [ 25 ], showed the existence of a Hopf bifurcation in a model of EIAV infection with a delay in the CTL response [ 26 ], and determined the number of vaccinations needed to prevent mutant escape [ 27 ].…”

Section: Introductionmentioning

confidence: 99%

Key Factors and Parameter Ranges for Immune Control of Equine Infectious Anemia Virus Infection

Hull-Nye

Meadows

Smith

et al. 2023

Viruses

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Equine Infectious Anemia Virus (EIAV) is an important infection in equids, and its similarity to HIV creates hope for a potential vaccine. We analyze a within-host model of EIAV infection with antibody and cytotoxic T lymphocyte (CTL) responses. In this model, the stability of the biologically relevant endemic equilibrium, characterized by the coexistence of long-term antibody and CTL levels, relies upon a balance between CTL and antibody growth rates, which is needed to ensure persistent CTL levels. We determine the model parameter ranges at which CTL and antibody proliferation rates are simultaneously most influential in leading the system towards coexistence and can be used to derive a mathematical relationship between CTL and antibody production rates to explore the bifurcation curve that leads to coexistence. We employ Latin hypercube sampling and least squares to find the parameter ranges that equally divide the endemic and boundary equilibria. We then examine this relationship numerically via a local sensitivity analysis of the parameters. Our analysis is consistent with previous results showing that an intervention (such as a vaccine) intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. Finally, we show that the CTL production rate can entirely determine the long-term outcome, regardless of the effect of other parameters, and we provide the conditions for this result in terms of the identified ranges for all model parameters.

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“…Schwartz et al described infection in the context of sensitive or NAb-resistant strains, both in the presence of EIAV-specific antibodies [17] and with different modes of transmission [18], in order to better quantify lentivirus escape from antibody responses [19]. Geethamalini and Balamuralitharan studied a variety of theoretical models for EIAV and focused on mathematical analyses to determine semianalytical solutions and global stability of equilibria using homotopy analysis [20] to estimate parameters [21] and to show the existence of a Hopf bifurcation [22].…”

Section: Introductionmentioning

confidence: 99%

Modelling Mutation in Equine Infectious Anemia Virus Infection Suggests a Path to Viral Clearance with Repeated Vaccination

Schwartz

Costris-Vas

Smith

2021

Viruses

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Equine Infectious Anemia Virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions have been shown to block both wild-type and mutant virus infection, but the mutant sometimes escapes. Using these data, we develop a mathematical model that describes the interactions between antibodies and both wild-type and mutant virus populations, in the context of continual virus mutation. The aim of this work is to determine whether repeated vaccinations through antibody infusions can reduce both the wild-type and mutant strains of the virus below one viral particle, and if so, to examine the vaccination period and number of infusions that ensure eradication. The antibody infusions are modelled using impulsive differential equations, a technique that offers insight into repeated vaccination by approximating the time-to-peak by an instantaneous change. We use impulsive theory to determine the maximal vaccination intervals that would be required to reduce the wild-type and mutant virus levels below one particle per horse. We show that seven boosts of the antibody vaccine are sufficient to eradicate both the wild-type and the mutant strains. In the case of a mutant virus infection that is given infusions of antibodies targeting wild-type virus (i.e., simulation of a heterologous infection), seven infusions were likewise sufficient to eradicate infection, based upon the data set. However, if the period between infusions was sufficiently increased, both the wild-type and mutant virus would eventually persist in the form of a periodic orbit. These results suggest a route forward to design antibody-based vaccine strategies to control viruses subject to mutant escape.

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Semianalytical solutions by homotopy analysis method for EIAV infection with stability analysis

Cited by 13 publications

References 33 publications

Homotopy-Sumudu transforms for solving system of fractional partial differential equations

Homotopy-Sumudu transforms for solving system of fractional partial differential equations

Key Factors and Parameter Ranges for Immune Control of Equine Infectious Anemia Virus Infection

Modelling Mutation in Equine Infectious Anemia Virus Infection Suggests a Path to Viral Clearance with Repeated Vaccination

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