Dynamics of a Viral Infectiology Under Treatment

Ahmed, Shohel; Kamrujjaman, Md.; Rahman, Sejuti

doi:10.11948/20190209

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…Hence, dV 1 dt < 0 whenever R 0 ≤ 1. And, when S = S 0 , V = V 0 , I = 0; we calculate, dV 1 dt = 0 and vice-versa. Consequently, the singleton E 0 is the greatest compact invariant set in {(S, V, I) ∈ C( , R 3 + ) : dV 1 dt = 0}.…”

Section: Proof Of Theorem 33: Let Define a Lyapunov Function Asmentioning

confidence: 99%

“…Recently, many researchers have considered spatial structure as a central factor because it affects the spatial spreading of disease [1,2,6,14,15,24,38,39]. In this paper, we propose a spatially dependent vaccination model which is a diffusive version of the above model (1), where we consider the individual movements of all three compartment cells.…”

Section: Introductionmentioning

confidence: 99%

“…The notion is a spatial habitat in R n with a smooth boundary ∂ , is the usual Laplacian Operator, and δ 1 , δ 2 and δ 3 are the diffusion rates of susceptible, vaccinated and infectious compartments respectively. Since the model monitors dynamics of population, it follows that all its dependent variables and parameters, for examples, a, b, c, m, n, q 1 and q 2 must be non-negative as in the non-spatial model (1). We also set the upper bound of c as c < c * , which can be found in the proof of Lemma A.1.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a diffusive vaccination model with therapeutic impact and non-linear incidence in epidemiology

Kamrujjaman

Mahmud

Islam

2020

Journal of Biological Dynamics

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In this paper, we study a more general diffusive spatially dependent vaccination model for infectious disease. In our diffusive vaccination model, we consider both therapeutic impact and nonlinear incidence rate. Also, in this model, the number of compartments of susceptible, vaccinated and infectious individuals are considered to be functions of both time and location, where the set of locations (equivalently, spatial habitats) is a subset of R n with a smooth boundary. Both local and global stability of the model are studied. Our study shows that if the threshold level R 0 ≤ 1, the disease-free equilibrium E 0 is globally asymptotically stable. On the other hand, if R 0 > 1 then there exists a unique stable disease equilibrium E * . The existence of solutions of the model and uniform persistence results are studied. Finally, using finite difference scheme, we present a number of numerical examples to verify our analytical results. Our results indicate that the global dynamics of the model are completely determined by the threshold value R 0 .

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Section: Proof Of Theorem 33: Let Define a Lyapunov Function Asmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of a diffusive vaccination model with therapeutic impact and non-linear incidence in epidemiology

Kamrujjaman

Mahmud

Islam

2020

Journal of Biological Dynamics

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Optimal treatment strategies to control acute HIV infection

Ahmed

Rahman

Kamrujjaman

2021

Infectious Disease Modelling

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Various antiretroviral therapies (ART) are administered to symptomatic human immunodeficiency virus (HIV) infected individuals to improve their health. The treatment effectiveness may depend on suppressing development of drug resistance, reduce evolution of new viral strains, minimize serious side effects and the costs of drugs. This paper deals with some results concerning optimal drug administration scheme successful in improving patients' health especially in poorly resourced settings. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, and the free viruses. Generally, in viral infection, the drug strategy aspects either the virus infectivity or reduce the virion production. The mathematical model proposed here, deals with both situations with the objective function based on a combination of maximizing benefit relied on T cells count (the white cells that coordinate activities of the immune system) and minimizing the systemic cost. The existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward sweep method (FBSM). Our results indicate that early initiation of treatment makes a profound impact in both improving the quality of life and reducing the economic costs of therapy.

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Counterfeit/Fake and Substandard Medicines – A Global Bioethical Issue Requiring A Global Approach

Sarwar¹

2021

J Heal Ethics Admin

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Counterfeit drugs are a global problem and a public health hazard. Nearly 10 percent of all medicines sold worldwide are fake, leading to an estimated 100,000 deaths each year, equating to an additional economic burden of close to $200 billion annually. Counterfeit medicines also thwart public health efforts to control infectious diseases like Covid-19 and Tuberculosis and lead to the worsening of other public health crises such as anti-microbial resistance (AMR). According to the CDC, more than 2.8 million antibiotic-resistant infections in the U.S each year, with more than 35,000 people dying, have been reported. Globalization and the internet's expansion have led to the rapid spreading of poor-quality medicines due to the high demand for cheap goods and lack of access - before adequate detection and intervention are possible. Moreover, selling counterfeit medicine is more profitable with lesser penalties, even in the U.S. As a clandestine market, there is no precise magnitude of how the counterfeit-medicine market flows. The WHO is alarmed by the lack of available data to demonstrate the extent and impact of fake/substandard medicines. Controlling counterfeit drugs' availability will not be easy; however, it has become necessary to protect public and global health. Through the lens of a case in Bangladesh that demonstrates how easy it is to sell and get away with selling fake medicines in developing countries - this paper discusses how counterfeit medicines negatively contribute significantly to human lives and sufferings in developing and developed countries. No single policy will be effective based on the different issues faced on multiple fronts due to fake/substandard medicines. However, a broad-based concerted effort across the various stakeholders to combat this counterfeit drug problem and secure the global supply chain is urgently needed.

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Dynamics of a Viral Infectiology Under Treatment

Cited by 3 publications

References 21 publications

Dynamics of a diffusive vaccination model with therapeutic impact and non-linear incidence in epidemiology

Dynamics of a diffusive vaccination model with therapeutic impact and non-linear incidence in epidemiology

Optimal treatment strategies to control acute HIV infection

Counterfeit/Fake and Substandard Medicines – A Global Bioethical Issue Requiring A Global Approach

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