Assessing the Effects of Holling Type-II Treatment Rate on HIV-TB Co-infection

Tanvi,; Aggarwal, Rajiv

doi:10.1007/s10441-020-09385-w

Cited by 9 publications

(7 citation statements)

References 21 publications

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“…In our model, we have shown the trajectories corresponding to HIV and TB for four different values of the order of derivatives (α), to represent the role that memory plays in the treatment and recovery from HIV and TB infection and also in the stability of the equilibrium points. The different behaviors of solution trajectories, corresponding to the HIV-TB model for different values of the order of derivatives, indicate the novelty of this article over other papers on HIV-TB coinfection [14,44].…”

Section: Numerical Simulationsmentioning

confidence: 85%

“…The results obtained in other papers on HIV-TB coinfection have been proved for integer order only rather than fractional order. Tanvi et al [14] and Kumar and Jain [44] have considered HIV-TB co-infection models with integer order derivatives. They have shown the trajectories corresponding to HIV and TB co-infection for integer order.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Collaborative anti-TB and HIV activities such as HIV testing, antiretroviral therapy and TB preventive measures are required for the reduction in HIV-TB co-infection prevalence. The emergent requirement by the healthcare authorities led many researchers to work upon various infectious diseases including HIV-TB co-infection with an aim to provide strategies and control policies which reduce the transmission of HIV-TB co-infection [4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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A fractional order HIV-TB co-infection model in the presence of exogenous reinfection and recurrent TB

2021

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In this article, a novel fractional order model has been introduced in Caputo sense for HIV-TB co-infection in the presence of exogenous reinfection and recurrent TB along with the treatment for both HIV and TB. The main aim of considering the fractional order model is to incorporate the memory effect of both diseases. We have analyzed both sub-models separately with fractional order. The basic reproduction number, which measures the contagiousness of the disease, is determined. The HIV sub-model is shown to have a locally asymptotically stable disease-free equilibrium point when the corresponding reproduction number, R H , is less than unity, whereas, for R H > 1, the endemic equilibrium point comes into existence. For the TB sub-model, the disease-free equilibrium point has been proved to be locally asymptotically stable for R T < 1. The existence of TB endemic equilibrium points in the presence of reinfection and recurrent TB for R T < 1 justifies the existence of backward bifurcation under certain restrictions on the parame-

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Section: Numerical Simulationsmentioning

confidence: 85%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A fractional order HIV-TB co-infection model in the presence of exogenous reinfection and recurrent TB

2021

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“…Mathematical modeling provides an efficient way to analyze the real world problems such as the prediction of COVID-19 prevalence under certain assumptions. In order to model the real life problems more practically, a number of mathematical models have been proposed by various researchers with the time dependent parameters such as time dependent treatment rates and transmission rates to study the transmission dynamics of infectious diseases 1 , 25 – 28 . Many researchers are working in this direction to predict the severity and analyze the transmission dynamics of COVID-19 2 , 5 , 10 , 12 – 14 , 16 , 17 , 21 , 22 , 29 – 31 , 33 , 37 .…”

Section: Introductionmentioning

confidence: 99%

Optimal control strategies on COVID-19 infection to bolster the efficacy of vaccination in India

Rajput

Sajid

Tanvi

et al. 2021

Sci Rep

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The Novel Coronavirus which emerged in India on January/30/2020 has become a catastrophe to the country on the basis of health and economy. Due to rapid variations in the transmission of COVID-19, an accurate prediction to determine the long term effects is infeasible. This paper has introduced a nonlinear mathematical model to interpret the transmission dynamics of COVID-19 infection along with providing vaccination in the precedence. To minimize the level of infection and treatment burden, the optimal control strategies are carried out by using the Pontryagin’s Maximum Principle. The data validation has been done by correlating the estimated number of infectives with the real data of India for the month of March/2021. Corresponding to the model, the basic reproduction number $${\mathcal {R}}_0$$ R 0 is introduced to understand the transmission dynamics of COVID-19. To justify the significance of parameters we determined the sensitivity analysis of $${\mathcal {R}}_0$$ R 0 using the parameters value. In the numerical simulations, we concluded that reducing $${\mathcal {R}}_0$$ R 0 below unity is not sufficient enough to eradicate the COVID-19 disease and thus, it is required to increase the vaccination rate and its efficacy by motivating individuals to take precautionary measures.

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“…Tanvi and Aggarwal [37] proposed a non-linear mathematical model for HIV-TB co-infection with a constant time delay parameter defined as the delay in detection and initiation of treatment for coinfected cases. Tanvi et al [38] a model of HIV-TB co-infection with a non-linear treatment rate for TB was explored and conclude that to reduce the co-infection programs that accelerate TB treatment need to be implemented. Tanvi et al [39] explored a model of HIV/AIDS and TB co-infection with detection and treatment of both diseases, performed an optimal control analysis using the maximum principle of Pontryagin and showed the importance of accelerating the detection of cases of both diseases along with the treatment to reduce co-infection.…”

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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Assessing the Effects of Holling Type-II Treatment Rate on HIV-TB Co-infection

Cited by 9 publications

References 21 publications

A fractional order HIV-TB co-infection model in the presence of exogenous reinfection and recurrent TB

A fractional order HIV-TB co-infection model in the presence of exogenous reinfection and recurrent TB

Optimal control strategies on COVID-19 infection to bolster the efficacy of vaccination in India

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

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