Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

Khan, Karim M.; Zarin, Rahat; Khan, Amir; Yusuf, Abdullahi; Al-Shomrani, M. M.; Ullah, Arif

doi:10.1186/s13662-021-03249-4

Cited by 18 publications

(4 citation statements)

References 29 publications

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“…1) achieves global asymptotic stability at the endemic equilibrium. Proof: We prove the global stability of endemic equilibrium Pp under the above conditions by using geometrical approach [32,34,35], which is the generalization of Lyapunov theory in essence, by using the third additive compound matrix. Consider the subsystems of system (Eq.…”

Section: Stability Of Endemic Equilibriummentioning

confidence: 99%

Dynamic analysis and optimal control of worm propagation model with saturated incidence rate

Wang

Xue

2023

Front. Phys.

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In order to prevent the propagation of computer worms effectively, based on the latent character of worms, the exposed compartments of computer and USB device are introduced respectively, and a series of computer worm propagation models with saturation incidence rate are proposed. The qualitative behavior of the proposed model is studied. Firstly, the threshold R0 of the model is derived by using the next-generation matrix method, which completely characterized the stability of disease free equilibrium and endemic equilibrium. If R0 < 1, the disease free equilibrium is asymptotically stable, implying that the worm dies out eventually and its attack remains under control; if R0 > 1, the asymptotic stability of endemic equilibrium under certain conditions is proved, which means that the worm is always persistent and uncontrollable under such conditions. Secondly, the theoretical results are verified by numerical study, in which the relative importance of each parameter in worm prevalence is evaluated by sensitivity analysis. Finally, so as to minimize the number of computer and USB device carrying computer worms in short span of time, the worm propagation model is extended to incorporate three control strategies. The Pontryagin’s maximum principle is used to characterize the controls’ optimal levels. According to the control effect diagram, the combined strategy is effective in minimizing the transmission dynamics of worm virus in computer and USB devices populations respectively.

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Section: Stability Of Endemic Equilibriummentioning

confidence: 99%

Dynamic analysis and optimal control of worm propagation model with saturated incidence rate

Wang

Xue

2023

Front. Phys.

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“…We use two control variables i.e. social distancing and treatment [ 33 – 35 ]. The objective functional is Subject to the state system, model ( 2 ) is modified to ( 55 ) after incorporating the control variable with ICs …”

Section: Optimal Control Analysismentioning

confidence: 99%

Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

et al. 2021

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In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray–Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik–Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.

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“…The model based on the blood and liver using the FO derivative is presented by Jajarmi et al [29]. Moreover, FO derivatives have been used in the spread of the dengue fever [30] and many other of utmost significance [31][32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Numerical Procedure for Fractional HBV Infection with Impact of Antibody Immune

Noinang¹,

Sabir²,

Raja³

et al. 2023

Computers, Materials &Amp; Continua

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The current investigations are presented to solve the fractional order HBV differential infection system (FO-HBV-DIS) with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation (LMB) neural networks (NNs), i.e., LMBNNs. The FO-HBV-DIS with the response of antibody immune is categorized into five dynamics, healthy hepatocytes (H), capsids (D), infected hepatocytes (I), free virus (V) and antibodies (W). The investigations for three different FO variants have been tested numerically to solve the nonlinear FO-HBV-DIS. The data magnitudes are implemented 75% for training, 10% for certification and 15% for testing to solve the FO-HBV-DIS with the response of antibody immune. The numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton approach. To authenticate the validity, competence, consistency, capability and exactness of the LMBNNs, the numerical presentations using the mean square error (MSE), error histograms (EHs), state transitions (STs), correlation and regression are accomplished.

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Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

Cited by 18 publications

References 29 publications

Dynamic analysis and optimal control of worm propagation model with saturated incidence rate

Dynamic analysis and optimal control of worm propagation model with saturated incidence rate

Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

Numerical Procedure for Fractional HBV Infection with Impact of Antibody Immune

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