Numerical treatment of a nonlinear dynamical Hepatitis-B model: an evolutionary approach

Hepatitis-B is the world’s number one public health epidemic. Vast population of infects in developing countries is yet at risk. Generally, the mathematical model of Hepatitis-B is nonlinear and therefore changeable to solve by traditional analytical and finite difference schemes by processing all properties of model like boundedness, positivity, feasibility. In this paper, an unconditionally convergent semi-analytical approach based on modern evolutionary computational technique and Pade approximation (EPA) has been implemented for the treatment of nonlinear Hepatitis-B model. The convergence solution of EPA scheme on different compartments of population has been studied and found to be significant with robust and durable solution. Eventually, EPA reduces contaminated levels very rapidly, without the need to supply step size.

[1]  A. Atangana,et al.  Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data , 2020 .

[2]  Saeid Abbasbandy,et al.  Valid implementation of Sinc-collocation method to solve the fuzzy Fredholm integral equation , 2020, J. Comput. Appl. Math..

[3]  Parvaiz Ahmad Naik,et al.  Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control , 2020, Chaos, Solitons & Fractals.

[4]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[5]  F. Meurice,et al.  Five-year post vaccination efficacy of hepatitis B vaccine in rural Nigeria , 2011, Human vaccines.

[6]  M. Raja,et al.  Wavelets optimization method for evaluation of fractional partial differential equations: an application to financial modelling , 2018 .

[7]  Parvaiz Ahmad Naik,et al.  Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells , 2020 .

[8]  A. Guyton,et al.  Text book of medical physiology , 2013 .

[9]  H. Te,et al.  Epidemiology of hepatitis B and C viruses: a global overview. , 2010, Clinics in liver disease.

[10]  Lan Zou,et al.  Modeling the transmission dynamics and control of hepatitis B virus in China. , 2010, Journal of theoretical biology.

[11]  D. Labadarios,et al.  South African National HIV Prevalence, Incidence and Behaviour Survey, 2012 , 2014 .

[13]  N. Sene,et al.  Analysis of fractional fishery model with reserve area in the context of time-fractional order derivative , 2020 .

[14]  Mehmet Yavuz,et al.  Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method , 2020, Axioms.

[15]  Sania Qureshi,et al.  Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan , 2020, Math. Comput. Simul..

[16]  Edward A. Bender,et al.  An introduction to mathematical modeling , 1980 .

[17]  S. Iqbal,et al.  Numerical treatment of nonlinear model of virus propagation in computer networks: an innovative evolutionary Padé approximation scheme , 2018, Advances in Difference Equations.

[18]  A. Guyton,et al.  Textbook of Medical Physiology , 1961 .

[19]  M. A. Araghi,et al.  Fibonacci-regularization method for solving Cauchy integral equations of the first kind , 2017 .

[20]  N. Sene.  Fractional diffusion equation with new fractional operator , 2020 .

[21]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[22]  M. F. Tabassum,et al.  Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation , 2020 .

[23]  Deborah Lacitignola,et al.  On the dynamics of an SEIR epidemic model with a convex incidence rate , 2008 .

[24]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[25]  D. Celentano,et al.  Does marital status matter in an HIV hyperendemic country? Findings from the 2012 South African National HIV Prevalence, Incidence and Behaviour Survey , 2016, AIDS care.

[26]  Lequan Min,et al.  Global stability of endemic equilibrium point of basic virus infection model with application to HBV infection , 2010, J. Syst. Sci. Complex..

[27]  K. Kaita,et al.  A mathematical model to study the effect of hepatitis B virus vaccine and antivirus treatment among the Canadian Inuit population , 2009, European Journal of Clinical Microbiology & Infectious Diseases.

[28]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[29]  Salman Ahmadi-Asl,et al.  A New Extended Padé Approximation and Its Application , 2013, Adv. Numer. Anal..

[30]  Sujin Bureerat,et al.  Solving Partial Differential Equations Using a New Differential Evolution Algorithm , 2014 .