Stability and bifurcation analysis of a fractional‐order model of cell‐to‐cell spread of HIV‐1 with a discrete time delay

Abbas, Syed; Tyagi, Swati; Kumar, Pushpendra; Ertürk, Vedat Suat; Momani, Shaher

doi:10.1002/mma.8226

Cited by 23 publications

(13 citation statements)

References 34 publications

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“…Mathematical modeling approach research done by scholars using a deterministic method [10,14], a stochastic method [7,22], or a fractional order method [23][24][25][26][27][28][29][30][31][32] has made a great contribution to linking the scientific approach with real-world physical situations and also for the decision-making process for solving real-world problems [33]. Different scholars have formulated and analyzed mathematical models on COVID-19 transmission [7, 8, 22, 24-26, 29, 30, 34-37], syphilis transmission [10,[17][18][19]23], and other infectious diseases transmission [20, 21,27,28,33,[38][39][40]; however, no one has done analysis on COVID-19 and syphilis co-infection transmission dynamics.…”

Section: Introductionmentioning

confidence: 99%

COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

Teklu

Terefe²

2023

Front. Appl. Math. Stat.

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In this study, we have proposed and analyzed a new COVID-19 and syphilis co-infection mathematical model with 10 distinct classes of the human population (COVID-19 protected, syphilis protected, susceptible, COVID-19 infected, COVID-19 isolated with treatment, syphilis asymptomatic infected, syphilis symptomatic infected, syphilis treated, COVID-19 and syphilis co-infected, and COVID-19 and syphilis treated) that describes COVID-19 and syphilis co-dynamics. We have calculated all the disease-free and endemic equilibrium points of single infection and co-infection models. The basic reproduction numbers of COVID-19, syphilis, and COVID-19 and syphilis co-infection models were determined. The results of the model analyses show that the COVID-19 and syphilis co-infection spread is under control whenever its basic reproduction number is less than unity. Moreover, whenever the co-infection basic reproduction number is greater than unity, COVID-19 and syphilis co-infection propagates throughout the community. The numerical simulations performed by MATLAB code using the ode45 solver justified the qualitative results of the proposed model. Moreover, both the qualitative and numerical analysis findings of the study have shown that protections and treatments have fundamental effects on COVID-19 and syphilis co-dynamic disease transmission prevention and control in the community.

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Section: Introductionmentioning

confidence: 99%

COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

Teklu

Terefe²

2023

Front. Appl. Math. Stat.

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“…They showed that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Different other types of fractional-order epidemic systems with delays were considered in earlier studies [3,6,13,[34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a fractional‐order SEIR epidemic model with general incidence rate and time delay

Gacem

Kouche

Aïnseba

2023

Math Methods in App Sciences

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In this paper, we investigate the qualitative behavior of a class of fractional SEIR epidemic models with a more general incidence rate function and time delay to incorporate latent infected individuals. We first prove positivity and boundedness of solutions of the system. The basic reproduction number  0 of the model is computed using the method of next generation matrix, and we prove that if  0 < 1, the healthy equilibrium is locally asymptotically stable, and when  0 > 1, the system admits a unique endemic equilibrium which is locally asymptotically stable. Moreover, using a suitable Lyapunov function and some results about the theory of stability of differential equations of delayed fractional-order type, we give a complete study of global stability for both healthy and endemic steady states. The model is used to describe the COVID-19 outbreak in Algeria at its beginning in February 2020. A numerical scheme, based on Adams-Bashforth-Moulton method, is used to run the numerical simulations and shows that the number of new infected individuals will peak around late July 2020. Further, numerical simulations show that around 90% of the population in Algeria will be infected. Compared with the WHO data, our results are much more close to real data. Our model with fractional derivative and delay can then better fit the data of Algeria at the beginning of infection and before the lock and isolation measures. The model we propose is a generalization of several SEIR other models with fractional derivative and delay in literature.

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“…Mathematical models are mainly used in virology to understand how viruses spread within a host and how the disease develops. In the literature, there are several HBV infection models [6][7][8] that explain the dynamics of the disease from various perspectives. For example, Nowak et al [9] proposed a mathematical model on viral dynamics in 1996, which is called the "basic model" of virus dynamics, considering susceptible cells, infected cells, and viruses.…”

Section: Introductionmentioning

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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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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Stability and bifurcation analysis of a fractional‐order model of cell‐to‐cell spread of HIV‐1 with a discrete time delay

Cited by 23 publications

References 34 publications

COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

Stability analysis of a fractional‐order SEIR epidemic model with general incidence rate and time delay

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

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