Application of homotopy analysis method for solving the SEIR models of epidemics

Momoh, Abdulfatai Atte; Ibrahim, M. O.; Tahir, AG; Adamu, Ibrahim Isa

doi:10.12988/nade.2015.3818

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…If the auxiliary linear operator, the initial guess, the auxiliary parameter h and the auxiliary function are properly chosen so that a) The solution ∅( ; ) of the zero-order deformation equation 11 According to equation (16), the governing equation can be deduced from the zero-order deformation equation (14).…”

Section: Basic Idea Of Homotopy Analysis Methodsmentioning

confidence: 99%

“…Other papers consulted and referenced are [2,8,9,12,16,19,20] In this paper, we modified the model of [23]and then solve it with HAM. The total population size N(t) is divided into four compartment, a susceptible compartment, labeled S,( in which all the individuals are vulnerable to the disease but are not yet infected with the disease), an exposed compartment, labeled E,( in which all the individuals are already infected with the disease but are not yet infectious, that is, they cannot infect others with the disease), an infected compartment, labeled I (in which all the individuals are infected by the disease and infectious), a recovered compartment, labeled R in which all the individuals are recovered from the disease and we assume that immunity is not permanent and that recovered individuals do revert to the susceptible class), hence joins the susceptible class again, S. Denote the numbers of individuals in the compartments S, E, I, R, and S, at time t as S(t), E(t), I(t), R(t), and S(t) respectively.…”

Section: Introductionmentioning

confidence: 99%

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Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Chioma¹,

Ugonna²,

Michael³

et al. 2019

MMA

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In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.

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Section: Basic Idea Of Homotopy Analysis Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Chioma¹,

Ugonna²,

Michael³

et al. 2019

MMA

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“…Moreover, to determine parameters for different infectious diseases, models employ simple assumptions or gathered statistics along with mathematics to measure the results of various interventions (2). Modeling can determine which intervention(s) may prevent, test, or forecast potential development trends (3).…”

Section: Introductionmentioning

confidence: 99%

Future of Mathematical Modelling: A Review of COVID-19 Infected Cases Using S-I-R Model

Yunus

Ibrahim

et al. 2021

Baghdad Sci.J

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The spread of novel coronavirus disease (COVID-19) has resulted in chaos around the globe. The infected cases are still increasing, with many countries still showing a trend of growing daily cases. To forecast the trend of active cases, a mathematical model, namely the SIR model was used, to visualize the spread of COVID-19. For this article, the forecast of the spread of the virus in Malaysia has been made, assuming that all Malaysian will eventually be susceptible. With no vaccine and antiviral drug currently developed, the visualization of how the peak of infection (namely flattening the curve) can be reduced to minimize the effect of COVID-19 disease. For Malaysians, let's ensure to follow the rules and obey the SOP to lower the R 0 value from time to time, hoping that the virus will vanish one day.

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Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

Bakare

Chakraverty

Potůček

2021

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This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model. Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. The results obtained were compared with the numerical solution and found to be in good agreement. Finally, various simulations were done to discuss the solution.

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Application of homotopy analysis method for solving the SEIR models of epidemics

Cited by 3 publications

References 15 publications

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Future of Mathematical Modelling: A Review of COVID-19 Infected Cases Using S-I-R Model

Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

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