A stochastic age-structured HIV/AIDS model based on parameters estimation and its numerical calculation

Abstract In this paper, we obtain the expressions of epidemiological parameters using a class of feedforward neural networks (FNNs) based on the data collected from Chinese Center for Disease Control and Prevention (CCDCP), and establish a stochastic age-structured HIV/AIDS model with parameter perturbation. In order to ensure the mathematical and epidemiological rationality of the model, we discuss the existence, uniqueness, and boundedness of its positive solution. Due to the difficulty of solving the true solution for the stochastic age-structured HIV/AIDS model, we propose a full-discrete scheme using the Galerkin finite element method in age discretization and the Euler’s scheme in time discretization. The error estimation between the numerical solution and the true solution is established. The results are justified by computer simulations.

[1]  Wan-Kai Pang,et al.  Exponential stability of numerical solutions for a class of stochastic age-dependent capital system with Poisson jumps , 2011, J. Comput. Appl. Math..

[2]  P. Chow Stochastic partial differential equations , 1996 .

[3]  Hisashi Inaba,et al.  Endemic threshold results in an age-duration-structured population model for HIV infection. , 2006, Mathematical biosciences.

[4]  F. Nyabadza,et al.  The dynamics of an HIV/AIDS model with screened disease carriers , 2009 .

[5]  J. Hyman,et al.  Using mathematical models to understand the AIDS epidemic , 1988 .

[6]  V. Thomée,et al.  The stability in _{} and ¹_{} of the ₂-projection onto finite element function spaces , 1987 .

[7]  Manmohan Singh,et al.  Parameter estimation of influenza epidemic model , 2013, Appl. Math. Comput..

[8]  F. Nyabadza A MATHEMATICAL MODEL FOR COMBATING HIV/AIDS IN SOUTHERN AFRICA: WILL MULTIPLE STRATEGIES WORK? , 2006 .

[9]  Ping Yan Impulsive SUI epidemic model for HIV/AIDS with chronological age and infection age. , 2010, Journal of theoretical biology.

[10]  Xu Yang,et al.  Strongly convergent error analysis for a spatially semidiscrete approximation of stochastic partial differential equations with non-globally Lipschitz continuous coefficients , 2021, J. Comput. Appl. Math..

[11]  Michelle Chen,et al.  A Model for Spheroid versus Monolayer Response of SK-N-SH Neuroblastoma Cells to Treatment with 15-Deoxy-PGJ 2 , 2016, Comput. Math. Methods Medicine.

[12]  Jiye Zhang,et al.  Absolute stability analysis in cellular neural networks with variable delays and unbounded delay , 2004 .

[13]  Li Wang,et al.  Modeling a stochastic age-structured capital system with Poisson jumps using neural networks , 2020, Inf. Sci..

[14]  J. Hyman,et al.  Threshold conditions for the spread of the HIV infection in age-structured populations of homosexual men. , 1994, Journal of theoretical biology.

[15]  Xuerong Mao,et al.  A Stochastic Differential Equation Model for the Spread of HIV amongst People Who Inject Drugs , 2016, Comput. Math. Methods Medicine.

[16]  Liangjian Hu,et al.  A Stochastic Differential Equation SIS Epidemic Model , 2011, SIAM J. Appl. Math..

[17]  Francisco Sandoval Hernández,et al.  Estimation of the Rate of Detection of Infected Individuals in an Epidemiological Model , 2007, IWANN.

[18]  Zhang Qi-min,et al.  Existence, uniqueness and exponential stability for stochastic age-dependent population , 2004 .

[19]  Claver P. Bhunu,et al.  Mathematical Analysis of an HIV/AIDS Model: Impact of Educational Programs and Abstinence in Sub-Saharan Africa , 2011, J. Math. Model. Algorithms.

[20]  Shengnan Zhao,et al.  Threshold behavior in a stochastic algal growth model with stoichiometric constraints and seasonal variation , 2020 .

[21]  C. Bhunu,et al.  Mathematical Analysis of a Two Strain HIV/AIDS Model with Antiretroviral Treatment , 2009, Acta Biotheoretica.

[22]  Sebastian Aniţa,et al.  Analysis and Control of Age-Dependent Population Dynamics , 2010 .

[23]  Liangjian Hu,et al.  Risk Analysis for AIDS Control Based on a Stochastic Model with Treatment Rate , 2009 .

[24]  X. Mao,et al.  Environmental Brownian noise suppresses explosions in population dynamics , 2002 .

[25]  X. Mao,et al.  A stochastic model of AIDS and condom use , 2007 .

[26]  Klaus Schittkowski,et al.  Numerical Data Fitting in Dynamical Systems , 2002 .

[27]  Miguel A. Atencia Ruiz,et al.  Estimation of parameters based on artificial neural networks and threshold of HIV/AIDS epidemic system in Cuba , 2013, Math. Comput. Model..

[28]  S. Busenberg,et al.  A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS. , 1991, IMA journal of mathematics applied in medicine and biology.

[29]  Winston Garira,et al.  Asymptotic properties of an HIV/AIDS model with a time delay , 2007 .

[30]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[31]  Qimin Zhang,et al.  Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion , 2008 .

[32]  Carlos Castillo-Chavez,et al.  Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission , 1992 .

[33]  M. Nöthen,et al.  Further evidence for the involvement of MYH9 in the etiology of non-syndromic cleft lip with or without cleft palate. , 2009, European journal of oral sciences.

[34]  Feilong Cao,et al.  Interpolation and rates of convergence for a class of neural networks , 2009 .

[35]  Qingshan Yang,et al.  Dynamics of a multigroup SIR epidemic model with stochastic perturbation , 2012, Autom..