Transmission dynamics of tuberculosis with multiple re-infections

Das, Dhiraj Kumar; Khajanchi, Subhas; Kar, Tapan Kumar

doi:10.1016/j.chaos.2019.109450

Cited by 61 publications

(22 citation statements)

References 31 publications

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“…The analysis focused on the applications of dynamical systems methods and optimal control theory to the epidemiology of TB. In agreement with the earlier studies on TB models with exogenous re‐infection property (see, for examples, References 3,4,6,9, and 13), it was shown that the autonomous deterministic TB model exhibits backward bifurcation whether incomplete treatment property is present or not. The occurrence of backward bifurcation in TB transmission dynamics makes the disease control more taxing.…”

Section: Resultssupporting

confidence: 90%

“…It should be mentioned here that the parameter values used for simulating Figure 1 are for illustration purpose only, and may not be epidemiologically realistic 24 . The epidemiological consequence of backward bifurcation phenomenon is that the classical requirement of

ℛ_{0} < 1

is, although necessary, not sufficient for the effective control of TB transmission in the population 3,6,9 …”

Section: Analysis Of Tb Model Without Controlsmentioning

confidence: 99%

“…A number of mathematical models have been developed to analyze the dynamical spread of TB in human population (see, eg, References 3‐11 and some of the references therein). In Reference 7, the authors presented a mathematical model for TB with exogenous re‐infection, which allows for the possibility of a subcritical bifurcation at a certain critical value of the basic reproduction number.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control analysis of a tuberculosis model with exogenous re‐infection and incomplete treatment

Abimbade

Olaniyi

Ajala

et al. 2020

Optim Control Appl Methods

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Summary A new mathematical model of tuberculosis (TB) featuring exogenous re‐infection and incomplete treatment is presented and analyzed. The model divides total population into susceptible, latently infected, actively infected (uninformed and enlightened), and treatment classes. The model with or without incomplete treatment exhibits backward bifurcation phenomenon, which is caused by the presence of exogenous re‐infection. However, further investigation reveals that the absence of incomplete treatment has the potential to reduce the backward bifurcation range significantly. The global dynamics of the TB model without exogenous re‐infection is completely determined by the basic reproduction number under certain modifications on parameters. Furthermore, the model is extended to include three time‐dependent control functions, such as public awareness campaign, treatment effort, and preventive control against incomplete treatment. The existence of the optimal control for the nonautonomous model is proven and the three controls are characterized using Pontryagin's maximum principle. Numerical simulations are performed to show the significance of singular implementation of each of the controls and combination of the three controls in minimizing the TB burden in the population.

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Section: Resultssupporting

confidence: 90%

ℛ_{0} < 1

is, although necessary, not sufficient for the effective control of TB transmission in the population 3,6,9 …”

Section: Analysis Of Tb Model Without Controlsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal control analysis of a tuberculosis model with exogenous re‐infection and incomplete treatment

Abimbade

Olaniyi

Ajala

et al. 2020

Optim Control Appl Methods

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“…The COVID-19 epidemic in India has attracted considerable interest thus far, with example ranging from the study of [47] . Mathematical modeling of infectious diseases with the effect of media is also an important factor to constrain the outbreak of the diseases [48] , [49] , [50] , [51] .…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the COVID-19 pandemic with intervention strategies

et al. 2021

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Mathematical modeling play an important role to better understand the disease dynamics and designing strategies to manage quickly spreading infectious diseases in lack of an effective vaccine or specific antivirals. During this period, forecasting is of utmost priority for health care planning and to combat against COVID-19 epidemic. In this study, we proposed and extended classical SEIR compartment model refined by contact tracing and hospitalization strategies to explain the COVID-19 outbreak. We calibrated our model with daily COVID-19 data for the five provinces of India namely, Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal and the overall India. To identify the most effective parameters we conduct a sensitivity analysis by using the partial rank correlation coefficients techniques. The value of those sensitive parameters were estimated from the observed data by least square method. We perform sensitivity analysis for to investigate the relative importance of the system parameters. Also, we compute the sensitivity indices for to determine the robustness of the model predictions to parameter values. Our study demonstrates that a critically important strategy can be achieved by reducing the disease transmission coefficient and clinical outbreak rate to control the COVID-19 outbreaks. Performed short-term predictions for the daily and cumulative confirmed cases of COVID-19 outbreak for all the five provinces of India and the overall India exhibit the steady exponential growth of some states and other states showing decays of daily new cases. Long-term predictions for the Republic of India reveals that the COVID-19 cases will exhibit oscillatory dynamics. Our research thus leaves the option open that COVID-19 might become a seasonal occurrence. Our model simulation demonstrates that the COVID-19 cases across India at the end of September 2020 obey a power law.

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“…We also note that people who chew Khat may return to vulnerable groups due to social, economic, environmental, and religious factors with a rate α 2 and constant and diverse population. In this study, we used a compartment model similar to SEIR [22][23][24][25][26][27][28][29]. In this deterministic model, we have considered a system of first-order nonlinear ordinary differential equations, which is derived and analyzed analytically and analyzed only numerically using Matlab ode45.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Analysis of Khat-Chewing Dynamics

Wubneh

Desta

Amsalu

2021

Journal of Mathematics

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Khat is a green leaf and greenish plant where its branches and leaves are chewed to discharge liquid having active chemicals that change the user’s mood. The purpose of this article is to develop and analyze a mathematical model that can be used to understand the dynamics of chewing Khat. The proposed model monitors the dynamics of five compartments, namely, a group of people who do not chew Khat, designated as N t ; a group of people who are surrounded by Khat chewers but do not chew at present and may chew Khat in the future, denoted this as Σ t ; a group of people who chew Khat, which is represented in C t ; a group of people contains individuals who consumed Khat quite temporarily for social, spiritual, and recreational purposes, and we describe this group in T t ; and a group of people those who constantly chew Khat, and they are denoted by H t . We determined the Khat chewing generation number R c 0 using the next-generation matrix method, and we have examined the biological meaningfulness, mathematical wellposedness, and stability of both Khat chewing-free and Khat chewing-present equilibrium points of the model analytically. Numerical simulations were presented by solving our dynamical system using Matlabode45 to check the analytical results by considering parameter estimations. The results of this study show that, for R c 0 = .00039 , the Khat chewing-free equilibrium point is stable, and it is unstable for R c 0 = 1.194 , and the Khat chewing-present equilibrium point is stable if R c 0 = 1.194 , and it is unstable if R c 0 = .00039 . The stability of both equilibrium points implies that, for a high rate of conversion from non-Khat chewer to exposed groups ρ , the inflow of an insignificant number of Khat chewers to the community produces a significant number of Khat chewers , and if the return back from Khat chewing to the exposed group because of socio-economic, environmental, and religious influences α 2 grows exponentially, the inflow of an insignificant number of Khat chewers to the community produces an insignificant number of Khat chewers. It is found that increasing the rate of conversion from non-Khat chewer to exposed groups ρ makes the disease eradication more challenging. We, therefore, strongly urge religious leaders, social committee leaders, elders, and health experts to teach their followers to reduce their Khat-chewing habits.

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Transmission dynamics of tuberculosis with multiple re-infections

Cited by 61 publications

References 31 publications

Optimal control analysis of a tuberculosis model with exogenous re‐infection and incomplete treatment

Optimal control analysis of a tuberculosis model with exogenous re‐infection and incomplete treatment

Mathematical modeling of the COVID-19 pandemic with intervention strategies

Mathematical Modeling and Analysis of Khat-Chewing Dynamics

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