Stability analysis and numerical simulations of spatiotemporal HIV CD4+ T cell model with drug therapy

Investigating the impact of stochasticity on HIV infection dynamics in CD4 + T cells using a reaction-diffusion model

The disease dynamics affect the human life. When one person is affected with a disease and if it is not treated well, it can weaken the immune system of the body. Human Immunodeficiency Virus (HIV) is a virus that attacks the immune system, of the body which is the defense line against diseases. If it is not treated well then HIV progresses to its advanced stages and it is known as Acquired Immunodeficiency Syndrome (AIDS). HIV is typically a disease that can transferred from one person to another in several ways such as through blood, breastfeeding, sharing needles or syringes, and many others. So, the need of the hour is to consider such important disease dynamics and that will help mankind to save them from such severe disease. For the said purpose the reaction-diffusion HIV CD4+ T cell model with drug therapy under the stochastic environment is considered. The underlying model is numerically investigated with two time-efficient schemes and the effects of various parameters used in the model are analyzed and explained in a real-life scenario. Additionally, the obtained results will help the decision-makers to avoid such diseases. The random version of the HIV model is numerically investigated under the influence of time noise in It o ^ sense. The proposed stochastic backward Euler (SBE) scheme and proposed stochastic Implicit finite difference (SIFD) scheme are developed for the computational study of the underlying model. The consistency of the schemes is proven in the mean square sense and the given system of equations is compatible with both schemes. The stability analysis proves that both schemes and schemes are unconditionally stable. The given system of equations has two equilibria, one is disease-free equilibrium (DFE) and the other is endemic equilibrium. The simulations are drawn for the different values of the parameters. The proposed SBE scheme showed the convergent behavior towards the equilibria for the given values of the parameters but also showed negative behavior that is not biological. The proposed SIFD scheme showed better results as compared with the stochastic SBE scheme. This scheme has convergent and positive behavior towards the equilibria points for the given values of the parameters. The effect of various parameters is also analyzed. Simulations are drawn to evaluate the efficacy of the schemes.

Gudermannian neural network procedure for the nonlinear prey-predator dynamical system

The present study performs the design of a novel Gudermannian neural networks (GNNs) for the nonlinear dynamics of prey-predator system (NDPPS). The process of GNNs is applied using the global and local search approaches named as genetic algorithm and interior-point algorithms, i.e., GNNs-GA-IPA. An error-based merit function is constructed using the NDPPS and its initial conditions and then optimized by the hybrid of GA-IPA. Six cases of the NDPPS using the variable coefficients have been presented and the correctness is observed through the overlapping of the obtained and Runge-Kutta reference results. The results of the NDPPS have been performed between 0 and 5 using the step size 0.02. The graph of absolute error are performed around 10-06 to 10-08 to check the consistency of the proposed GNNs-GA-IPA. The statistical analysis based minimum, median and semi-interquartile ranges have been performed for both predator and prey dynamics of the model. Moreover, the investigations through the statistical operators are performed to validate the reliability of the obtained outcomes based on multiple trials.

A Higher-Order Galerkin Time Discretization and Numerical Comparisons for Two Models of HIV Infection

Human immunodeficiency virus (HIV) infection affects the immune system, particularly white blood cells known as CD4+ T-cells. HIV destroys CD4+ T-cells and significantly reduces a human’s resistance to viral infectious diseases as well as severe bacterial infections, which can lead to certain illnesses. The HIV framework is defined as a system of nonlinear first-order ordinary differential equations, and the innovative Galerkin technique is used to approximate the solutions of the model. To validate the findings, solve the model employing the Runge-Kutta (RK) technique of order four. The findings of the suggested techniques are compared with the results obtained from conventional schemes such as MuHPM, MVIM, and HPM that exist in the literature. Furthermore, the simulations are performed with different time step sizes, and the accuracy is measured at various time intervals. The numerical computations clearly demonstrate that the Galerkin scheme, in contrast to the Runge-Kutta scheme, provides incredibly precise solutions at relatively large time step sizes. A comparison of the solutions reveals that the obtained results through the Galerkin scheme are in fairly good agreement with the RK4 scheme in a given time interval as compared to other conventional schemes. Moreover, having performed various numerical tests for assessing the efficiency and computational cost (in terms of time) of the suggested schemes, it is observed that the Galerkin scheme is noticeably slower than the Runge-Kutta scheme. On the other hand, this work is also concerned with the path tracking and damped oscillatory behaviour of the model with a variable supply rate for the generation of new CD4+ T-cells (based on viral load concentration) and the HIV infection incidence rate. Additionally, we investigate the influence of various physical characteristics by varying their values and analysing them using graphs. The investigations indicate that the lateral system ensured more accurate predictions than the previous model.

The stochastic bifurcation analysis and stochastic delayed optimal control for epidemic model with general incidence function

In the history of the world, contagious diseases have been proved to pose serious threats to humanity that needs uttermost research in the field and its prompt implementations. With this motive, an attempt has been made to investigate the spread of such contagion by using a delayed stochastic epidemic model with general incidence rate, time-delay transmission, and the concept of cross immunity. It is proved that the system is mathematically and biologically well-posed by showing that there exist a positive and bounded global solution of the model. Necessary conditions are derived, which guarantees the permanence as well as extinction of the disease. The model is further investigated for the existence of an ergodic stationary distribution and established sufficient conditions. The non-zero periodic solution of the stochastic model is analyzed quantitatively. The analysis of optimality and time delay is used, and a proper strategy was presented for prevention of the disease. A scheme for the numerical simulations is developed and implemented in MATLAB, which reflects the long term behavior of the model. Simulation suggests that the noises play a vital role in controlling the spread of an epidemic following the proposed flow, and the case of disease extinction is directly proportional to the magnitude of the white noises. Since time delay reflects the dynamics of recurring epidemics, therefore, it is believed that this study will provide a robust basis for studying the behavior and mechanism of chronic infections.