Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo-Fabrizio Derivative

Peripheral blood CD4+ T cell count predicts recurrence of condyloma acuminatum after photodynamic therapy in HIV-positive patients

BACKGROUND

Few studies have reported postoperative relapse of condyloma acuminatum (CA) after 5-aminolevulinic acid photodynamic therapy (ALA-PDT) in human immunodeficiency virus (HIV) positive patients.

METHODS

The clinical data of HIV-positive CA patients treated with ALA-PDT from October 2018 to December 2019 were analyzed retrospectively. Univariate and multivariate Cox regression was used to analyze the variables related to postoperative recurrence. Pearson correlation test was employed to analyze the correlation between CD4⁺ T cell count and postoperative recurrence rate. Kaplan-Meier method was used to compare the CA recurrence after ALA-PDT in low CD4 group and high CD4 group.

RESULTS

A total of 38 HIV-positive patients with CA were included in the study. Among them, 26 patients experienced CA recurrence within 6 months, and the recurrence rate was 68.4%. CD4⁺ T cell count was 187.0 (79.0-596.0) cells/μl in relapsed patients and 406.0 (89.0-612.0) cells/μl in non-relapsed patients, showing a statistically significant difference (p = .005). Pearson correlation coefficient analysis revealed a negative correlation between CD4⁺ T cell count and postoperative recurrence rate (p = .005, r = -.443). Univariate regression analysis showed that CD4⁺ T cell count was correlated with postoperative recurrence, hazard ratio (HR) was 0.99 [95% Confidence interval (CI) = 0.99-1.0, p = .012]. Multivariate Cox regression analysis showed that with the low CD4⁺ T cell count as the reference, the high CD4⁺ T cell count was negatively correlated with postoperative recurrence (HR = 0.09, 95% CI 0.01-0.87, p = .038).

CONCLUSIONS

Peripheral blood CD4⁺ T cell count can predict the CA recurrence rate after ALA-PDT in HIV-positive patients.

Analysis of the Fractional HIV Model under Proportional Hadamard-Caputo Operators

Modeling human immunodeficiency virus (HIV) via fractional operators has several benefits over the classical integer-order HIV model. The reason is that the fractional HIV model relies not only on the recent status but also on the former conduct of the model. Thus, we are motivated to introduce and analyze a new fractional HIV model. This article focuses on a novel fractional HIV model under the proportional Hadamard-Caputo fractional operators. The study of this model involves the existence and uniqueness (EU) of its solution and the stability examination. We employ Leray–Schauder nonlinear alternative (L-SNLA) and Banach’s fixed point theorems to analyze the EU results. In addition, for this provided model, we develop several forms of Ulam’s stability findings. As a special case of our results, we give and analyze a new fractional HIV model with Hadamard-Caputo operators. Moreover, by appropriate choice of the fractional parameters, the obtained outcomes are valid for analysis of the fractional HIV models formed by several fractional operators defined in the past literature.

Investigation of fractal-fractional HIV infection by evaluating the drug therapy effect in the Atangana-Baleanu sense

In this paper, we apply the fractal-fractional derivative in the Atangana-Baleanu sense to a model of the human immunodeficiency virus infection of CD$ 4^{+} $ T-cells in the presence of a reverse transcriptase inhibitor, which occurs before the infected cell begins producing the virus. The existence and uniqueness results obtained by applying Banach-type and Leray-Schauder-type fixed-point theorems for the solution of the suggested model are established. Stability analysis in the context of Ulam's stability and its various types are investigated in order to ensure that a close exact solution exists. Additionally, the equilibrium points and their stability are analyzed by using the basic reproduction number. Three numerical algorithms are provided to illustrate the approximate solutions by using the Newton polynomial approach, the Adam-Bashforth method and the predictor-corrector technique, and a comparison between them is presented. Furthermore, we present the results of numerical simulations in the form of graphical figures corresponding to different fractal dimensions and fractional orders between zero and one. We analyze the behavior of the considered model for the provided values of input factors. As a result, the behavior of the system was predicted for various fractal dimensions and fractional orders, which revealed that slight changes in the fractal dimensions and fractional orders had no impact on the function's behavior in general but only occur in the numerical simulations.

Analysis and dynamical behavior of a novel dengue model via fractional calculus

The infection of dengue is an intimidating vector-borne disease caused by a pathogenic agent that affects different temperature areas and brings many losses in human health and economy. Thus, it is valuable to identify the most influential parameters in the transmission process for the control of dengue to lessen these losses and to turn down the economic burden of dengue. In this research, we formulate the transmission phenomena of dengue infection with vaccination, treatment and reinfection via Atangana–Baleanu operator to thoroughly explore the intricate system of the disease. Furthermore, to come up with more realistic, dependable and valid results through fractional derivative rather than classical order derivative. The next-generation approach has been utilized to compute the basic reproduction number for the suggested fractional model, indicated by [Formula: see text]; moreover, we conducted sensitivity test of [Formula: see text] to recognize and point out the role of parameters on [Formula: see text]. Our numerical results predict that the reproduction number of the system of dengue infection can be controlled by controlling the index of memory. The uniqueness and existence result has been proved for the solution of the system. A novel numerical method is presented to highlight the time series of dengue system. Eventually, we get numerical results for different assumptions of [Formula: see text] with specifying factors to conceptualize the effect of [Formula: see text] on the dynamics. It has been noted that the fractional-order derivative offers realistic, clear-cut and valid information about the dynamics of dengue fever. Moreover, we note through our analysis that the input parameters’ index of memory, biting rate, transmission probability and recruitment rate of mosquitos can be used as control parameter to lower the level of infection.

Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination

New fractional operators have the aim of attracting nonlocal problems that display fractal behaviour; and thus fractional derivatives have applications in long-term relation description along with micro-scaled and macro-scaled phenomena. Formulated by fractional operators, the formulation of a dynamical system is used in applications for the description of systems with long-range interactions. Vector-borne illnesses are one of the world’s most serious public health issues with a large economic impact on the nations that are impacted. Population increase, urbanization, globalization, and a lack of public health infrastructure have all had a role in the introduction and reemergence of vector-borne illnesses during the last four decades. The control of these infections are important to lessen the economic burden of vector-borne diseases in infected regions. In this research work, we formulate the transmission process of Zika virus with the impact of sexual incidence rate and vaccination in terms of mathematics. We presented the fundamental theory of fractional operators Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) for the analysis of the proposed system. We examine our system of Zika infection and determined the endemic indicator through a next-generation matrix technique. The uniqueness and existence of the solution has been investigated through fixed point theory. Accordingly, a numerical method has been introduced to investigate the dynamical nature of the system and make a comparison of the outcomes of the operators. The impact of different input factors has been conceptualized through dynamical behaviour of the system. We observed that lowering the index of memory, the fractional system provides accurate results about the recommended Zika dynamics and dramatically reduces infected people. It has been proved that high efficacy of a vaccine can lower the level of infection. Moreover, the impact of other parameters on the system of Zika virus infection are highlighted through numerical results.

Predicting Parameters of Heat Transfer in a Shell and Tube Heat Exchanger Using Aluminum Oxide Nanofluid with Artificial Neural Network (ANN) and Self-Organizing Map (SOM)

This study is a model of artificial perceptron neural network including three inputs to predict the Nusselt number and energy consumption in the processing of tomato paste in a shell-and-tube heat exchanger with aluminum oxide nanofluid. The Reynolds number in the range of 150–350, temperature in the range of 70–90 K, and nanoparticle concentration in the range of 2–4% were selected as network input variables, while the corresponding Nusselt number and energy consumption were considered as the network target. The network has 3 inputs, 1 hidden layer with 22 neurons and an output layer. The SOM neural network was also used to determine the number of winner neurons. The advanced optimal artificial neural network model shows a reasonable agreement in predicting experimental data with mean square errors of 0.0023357 and 0.00011465 and correlation coefficients of 0.9994 and 0.9993 for the Nusselt number and energy consumption data set. The obtained values of eMAX for the Nusselt number and energy consumption are 0.1114, and 0.02, respectively. Desirable results obtained for the two factors of correlation coefficient and mean square error indicate the successful prediction by artificial neural network with a topology of 3-22-2.