Modeling and analysis of the fractional-order epidemic model to investigate mutual influence in HIV/HCV co-infection

Naik, Parvaiz Ahmad; Yeolekar, Bijal M.; Qureshi, Sania; Yeolekar, Mahesh; Madzvamuse, Anotida

doi:10.1007/s11071-024-09653-1

Cited by 11 publications

(1 citation statement)

References 72 publications

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“…Paper [37] presents the stability analysis of the dengue model with fractional order. Derivatives of fractional order have the ability to account for memory history and heritability [38], which is especially beneficial in studying the spread of infections over time. These can more effectively capture the long-range dependence traits of real-world epidemics [39], enhancing the precision of predictions and offering a more accurate depiction of disease transmission.…”

Section: Introductionmentioning

confidence: 99%

Caputo-Fabrizio Fractional Order Epidemiological Model of Tuberculosis Transmission along with Imperfect Vaccination, Exogenous Reinfection and Endogenous Reactivation

Nandi,

Saha,

Roy

2024

Preprint

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This study has been carried out on the dynamics of tuberculosis (TB) transmission considering vaccination, endogenous re-activation of the dormant infection, and exogenous re-infection. We can comprehend the behavior of TB under the influence of vaccination from this article. The theoretical analysis demonstrates that the disease-free equilibrium point is locally asymptotically stable and the fractional order system is Ulam-Hyers type stable. We compute the vaccination reproduction number (R_v) as well as the basic reproduction number (R_0) using the next-generation matrix (NGM) approach. Our findings indicate that vaccinating a limited segment of the population can effectively eradicate the disease. The Adams–Bashforth 3-step method has been used to obtain the numerical solution of our model. The numerical simulations presented at the end of this study show that vaccination can reduce the number of susceptible and infectious individuals in the population. Moreover, the graphical representations illustrate that the number of infected individuals rises due to both exogenous reinfection and endogenous reactivation.

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Section: Introductionmentioning

confidence: 99%

Caputo-Fabrizio Fractional Order Epidemiological Model of Tuberculosis Transmission along with Imperfect Vaccination, Exogenous Reinfection and Endogenous Reactivation

Nandi,

Saha,

Roy

2024

Preprint

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Global Analysis of a Fractional‐Order Hepatitis B Virus Model Under Immune Response in the Presence of Cytokines

Naik,

Yeolekar,

Qureshi

et al. 2024

Advcd Theory and Sims

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This research proposes and investigates an epidemiological model to study the dynamic behaviors of the Hepatitis B virus (HBV) under immune response and cytokine influence. The model's stability, positivity, boundedness, and equilibria are analyzed using Lyapunov functional methods and the Routh–Hurwitz criterion under Caputo fractional derivative. The study evaluates nucleoside analogues and interferon treatments, determining critical drug efficiencies. Equilibria, including infection‐free and endemic states, are analyzed using the fundamental reproduction number, , to predict disease elimination. Numerical simulations utilize the fractional Adams method and the L1 scheme, capturing memory traces as the fractional order changes. Results show the L1 scheme effectively captures memory traces, providing empirical support for the theoretical findings. Furthermore, Ulam–Hyers stability is treated according to the equilibrium point, which describes relationships between functions. Notably, the findings of the study yielded profound insights. They revealed that the HBV system remains locally asymptotic stable at disease‐free and the endemic point when . At the same time, the simulations illustrated a correlation between the rate of infection and the rise in infected individuals, indicating the feasibility of eradicating and effectively managing HBV infections through a multifaceted approach and various measures such as vaccination and effective drug administration protocols. The proposed framework can guide medical professionals and decision‐makers in developing effective strategies to limit and eliminate the spread of HBV in the population.

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Generalised Neuronal Calcium Dynamics of Membrane and ER in the Polar Dimension

Vatsal,

Jha,

Singh

2024

Cell Biochem Biophys

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Modeling and analysis of the fractional-order epidemic model to investigate mutual influence in HIV/HCV co-infection

Cited by 11 publications

References 72 publications

Caputo-Fabrizio Fractional Order Epidemiological Model of Tuberculosis Transmission along with Imperfect Vaccination, Exogenous Reinfection and Endogenous Reactivation

Caputo-Fabrizio Fractional Order Epidemiological Model of Tuberculosis Transmission along with Imperfect Vaccination, Exogenous Reinfection and Endogenous Reactivation

Global Analysis of a Fractional‐Order Hepatitis B Virus Model Under Immune Response in the Presence of Cytokines

Generalised Neuronal Calcium Dynamics of Membrane and ER in the Polar Dimension

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