A fractional order differential equation model for Hepatitis B virus with saturated incidence

Simelane, Simphiwe; Dlamini, Phumlani

doi:10.1016/j.rinp.2021.104114

Cited by 19 publications

(7 citation statements)

References 29 publications

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“…In literature, most of the mathematical models [28,35,36] described the viral dynamics using fractional differential equations with commensurate order. The authors of these articles overlooked the fact that cells and viruses have different capacities to store memories and experiences.…”

Section: Modified Model With Incommensurate Order Of Fractional Deriv...mentioning

confidence: 99%

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Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Sutradhar,

Dalal

2023

Math Methods in App Sciences

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Hepatitis B virus (HBV) infection is a major public health concern throughout the world. It can be treated effectively through proper medication and vaccination, although it is very difficult to cure, especially in people who have had the chronic infection. So, it is necessary to pay proper attention for its eradication. In this study, two nonlinear fractional‐order HBV infection models with recycling effects of capsids are presented via the Caputo derivative. Each model contains four compartments, namely, susceptible hepatocytes, infected hepatocytes, HBV capsids, and viruses. In the first model, the order of fractional derivatives is equal for each compartment, whereas, in the second model, the order is incommensurate. The existence and uniqueness of solutions for both models are discussed separately. The parameters are estimated in order to validate the proposed model with experimental data obtained from a chimpanzee. Stability analyses are carried out for both models theoretically. The models are solved numerically using the predictor–corrector Adams–Bashforthm–Moulton method (for commensurate order) and implicit product integration of trapezoidal type method (for incommensurate order) with various choices of fractional orders and initial conditions. All the results are presented graphically. Interestingly, the results reveal the importance of fractional‐order derivatives in capturing the dynamics of HBV transmission in the host. It is also noticed that with the decrease in the order of fractional derivative, the peak level of infection decreases, but the disease takes a long time to be cured.

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Section: Modified Model With Incommensurate Order Of Fractional Deriv...mentioning

confidence: 99%

“…In addition, a few works on HBV infection considering fractional derivatives are available, for example, Nadia et al [16], Cardoso et al [28], Danane et al [35], and Simelane and Dlamini [36]. All of them have considered the commensurate order in their models.…”

Section: Comparison With Existing Modelsmentioning

confidence: 99%

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Sutradhar,

Dalal

2023

Math Methods in App Sciences

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“…Fractional order calculus are popular field that describe the application of non-integer order derivative in disease dynamics [29]. From literature, it is believed that modeling of physical and real problems using non-integer order derivative is more precise compared to integer-order derivatives [30], [58]. The main advantages of using fractional order derivative in disease dynamics is that, they can properly capture the memory effects and hereditary properties of species that exist in biological systems [31], [32], [54], [15], [58].…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics of Fractional-order Model for Malaria Disease Transmission

Helikumi

Lolika

2022

ARJOM

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In this study, we formulated and analyzed a fractional-order model for malaria disease transmission using Atangana-Beleanu-Caputo in sense to study the effects of heterogeneity vector biting exposure on the human population. To capture effects the heterogeneity vector biting exposure, we sub-divided the human population into two sub-groups namely; the population in high and low risk areas. In the model analysis, we computed the basic reproduction number R0 and qualitatively used to assess the existence and extinction of disease in the population. Additionally, we used the fixed point theorem to prove the existence and uniqueness of solutions.Numerical schemes for both Euler and Adam-Bathforth-Moulton are present in details and used in model simulations. Furthermore, we performed the numerical simulation to support the analytical results in this study. From numerical simulations, we estimated the values of model parameters using least square fitting method for the real data of malaria reported in Zimbabwe. The sensitivity analysis of the model parameters was done to determine the correlation between model parameters and R0: Finally, we used the Euler and Adam-Bashforth-Moulton scheme to simulate the model system using estimated parameters. Overall, we noted that fractional-order derivatives have more in uence on the dynamics of malaria disease in the population.

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“…Mathematical modeling is one of the most effective methods for forecasting of infectious disease outbreaks and, thus, yielding valuable insights to suggest how future efforts may be improved. An important method for epidemiological studies of such acute infectious diseases is mathematical modeling (3)(4)(5)(6). Therefore, it is necessary to establish a mathematical model to accurately predict the evolution trend of COVID-19 in the United States, and find key factors that can significantly affect the evolution of COVID-19 to provide effective control strategies.…”

Section: Introductionmentioning

confidence: 99%

Modeling the COVID-19 Epidemic With Multi-Population and Control Strategies in the United States

Sun

Long

Liu

2022

Front. Public Health

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As of January 19, 2021, the cumulative number of people infected with coronavirus disease-2019 (COVID-19) in the United States has reached 24,433,486, and the number is still rising. The outbreak of the COVID-19 epidemic has not only affected the development of the global economy but also seriously threatened the lives and health of human beings around the world. According to the transmission characteristics of COVID-19 in the population, this study established a theoretical differential equation mathematical model, estimated model parameters through epidemiological data, obtained accurate mathematical models, and adopted global sensitivity analysis methods to screen sensitive parameters that significantly affect the development of the epidemic. Based on the established precise mathematical model, we calculate the basic reproductive number of the epidemic, evaluate the transmission capacity of the COVID-19 epidemic, and predict the development trend of the epidemic. By analyzing the sensitivity of parameters and finding sensitive parameters, we can provide effective control strategies for epidemic prevention and control. After appropriate modifications, the model can also be used for mathematical modeling of epidemics in other countries or other infectious diseases.

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A fractional order differential equation model for Hepatitis B virus with saturated incidence

Cited by 19 publications

References 29 publications

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Global Dynamics of Fractional-order Model for Malaria Disease Transmission

Modeling the COVID-19 Epidemic With Multi-Population and Control Strategies in the United States

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