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

Farman, Muhammad; Tabassum, Muhammad Farhan; Naik, Parvaiz Ahmad; Akram, Sana

doi:10.1140/epjp/s13360-020-00902-x

Cited by 27 publications

(16 citation statements)

References 24 publications

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“…Farman et al (2020) proposed "numerical treatment of a nonlinear dynamical hepatitis-B model: an evolutionary approach" and implemented evolutionary computational technique and Padé approximation (EPA) for the treatment of nonlinear hepatitis-B model. ey concluded that evolutionary computational technique and Padé approximation (EPA) help to reduce contamination levels rapidly without the need to supply step size [18].…”

Section: Introductionmentioning

confidence: 99%

Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis

Wodajo

Mekonnen

2022

Journal of Mathematics

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Hepatitis B is a globally infectious disease. It is pretty contagious and can be transmitted by blood or bodily fluids, through things like sharing razors and toothbrushes. It has been called the silent killer because it is asymptomatic, one might have the virus but not know until it manifests itself until much later. Since people do not give attention, it will develop into cirrhosis and hepatocellular carcinoma that leads to liver transplantation and death. This nature of HBV disease motivated us to perform this work. Mathematical modeling of HBV transmission is an interesting research area. In this paper, we present characteristics of HBV virus transmission in the form of a mathematical model. We proposed and analyzed a compartmental nonlinear deterministic mathematical model SEACTR for transmission dynamics and control of hepatitis B virus disease. In this model, we used force infection which takes the contact rate of susceptible population and transmission probability into account. We proved that the solution of the considered dynamical system is positive and bounded. The model is studied qualitatively using the stability theory of differential equations and the effective reproductive number which represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The sensitivity index shows that the transfer rate from exposed class to acute infective class and transfer rate from exposed class to chronic infective class are the most dominant parameters contributing to the transmission of HBV. On the one hand, the vaccination rate and treatment rate are the parameters that suppress the transmission of the disease the most, and enhancing the vaccination rate for newborns and treatment for chronically infected individuals is very effective to stop the transmission of HBV. The combined efforts of vaccination, effective treatment, and interruption of transmission make elimination of the infection plausible and may eventually lead to the eradication of the virus.

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Section: Introductionmentioning

confidence: 99%

Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis

Wodajo

Mekonnen

2022

Journal of Mathematics

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“…The mathematical models for the study of epidemics have been widely spread, using different techniques and proposing methods to solve them and interpret the results [11][12][13][14][15]. For example, Naik et al [11] designed a fractional order model for HIV with the presence of prostitution in the population and studied prostitution in the spread of the disease.…”

Section: Introductionmentioning

confidence: 99%

“…Naik et al [12] designed and analyzed a non-linear fractional order model for HIV transmission which included an exposed compartment and divided the infected class of sex workers into conscious and unconscious infected. Farman et al [13] used evolutionary computational techniques and Padé's approach to give a semi-analytical approach in the treatment of a non-linear model for Hepatitis B. Naik et al [14] built and studied a model for the transmission of the COVID-19 epidemic of fractional order using the classical operator Caputo and operator Atangana-Baleanu-Caputo. Naik [15] studied an epidemic model of the SIR form with non-linear fractional order with Crowley-Martin type functional response and Holling type II treatment rate.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for the Study of Effectiveness in Therapy in Tuberculosis Taking into Account Associated Diseases

Moya¹,

Pietrus²,

Oliva³

2021

Contemporary Mathematics

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Tuberculosis (TB) remains a major global health problem. We present a deterministic mathematical model for the study of the effectiveness of therapy in TB to determine the impact of HIV/AIDS and diabetes in the spread of the disease and drug resistance. Our model takes into account the relationships between TB, HIV/AIDS, and diabetes and we also study the behavior of multidrug-resistance (MDR-TB) and extensively drug-resistant (XDR-TB). The main mathematical and epidemiology features of the model are investigated. The basic reproduction number (R0) in the different sub-populations (diabetics, HIV/AIDS, and those who do not suffer from these diseases) was studied. Conditions were obtained on the model parameters to know when the growth of the parameters associated with resistance to TB treatment has a negative impact on the transmission of TB in the population based on the R0 study. It is concluded that MDR-TB and XDR-TB have a negative impact on TB control. Computational simulations show that a greater number of drug-sensitive TB cases with respect to MDR-TB and XDR-TB cases are reported in the infected compartments, and MDR-TB cases surpass XDR-TB cases, except in the diabetes sub-population, which has a growth of XDR-TB cases that surpasses the other compartments of infected of all the sub-populations. It was shown when comparing the sub-populations of diabetes and HIV/AIDS, that although the diabetes sub-population reports a higher number of XDR-TB cases, a lower number of drug-sensitive TB and MDR-TB cases, have a greater number of recovered cases with respect to HIV/AIDS sub-population at the end of the study period. Also, when the XDR-TB cases in the diabetes sub-population exceed the other infected compartments, there is a growth of recovered TB in this subpopulation. The results suggest that it is necessary to increase the attention to the diabetic population, which include improved glucose control, increase the number of specialized medical consultations to achieve permanence in TB treatment and control the entry of individuals to the diabetic compartments by tests of diabetes.

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Section: Introductionmentioning

confidence: 99%

“…In recent years, the use of mathematical models with different techniques to predict the behavior of epidemics has been increasing [18,93,94]. For example, Farman et al [18] used evolutionary computational techniques and the Padé approach to study a nonlinear model of Hepatitis B. A. Omame et al [93] introduced and analyzed a model of human papillomavirus (HPV) and Chlamydia trachomatis co-infection, and studied different control strategies to eliminate HPV and Chlamydia trachomatis co-infections.…”

Section: Introductionmentioning

confidence: 99%

Mathematical models for the study of adherence to tuberculosis treatment taking into account the effects of HIV/AIDS and diabetes

Moya¹

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

Cited by 27 publications

References 24 publications

Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis

Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis

A Mathematical Model for the Study of Effectiveness in Therapy in Tuberculosis Taking into Account Associated Diseases

Mathematical models for the study of adherence to tuberculosis treatment taking into account the effects of HIV/AIDS and diabetes

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