Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis

Nkamba, Leontine Nkague; Manga, Thomas Timothee; Agouanet, Franklin; Manyombe, Martin Luther Mann

doi:10.1080/17513758.2018.1563218

Cited by 46 publications

(42 citation statements)

References 11 publications

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“…We carried out an uncertainty and sensitivity analysis using the Latin hypercube sampling (LHS), a statistical scheme for generating a sample of likely parameter values from a multidimensional distribution, and partial rank correlation coefficients (PRCCs), "a robust sensitivity measure for nonlinear but monotonic relationships between input and output, as long as little to no correlation exists between the inputs" [58][59][60][61], to identify model parameters that have most influence on the threshold R 0 and the COVID-19 transmission. Sensitivity analysis is useful and can help to identify parameters that need to be targeted in designing control strategies.…”

Section: Sensitivity Analysismentioning

confidence: 99%

A fractional order approach to modeling and simulations of the novel COVID-19

et al. 2020

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The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type susceptible–exposed–infected–recovered (SEIR) model to gain insight into the ongoing pandemic. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution profiles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as a valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduces the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

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Section: Sensitivity Analysismentioning

confidence: 99%

A fractional order approach to modeling and simulations of the novel COVID-19

et al. 2020

View full text Add to dashboard Cite

show abstract

“…We carried out an uncertainty and sensitivity analysis using the Latin hypercube sampling (LHS), a statistical scheme for generating a sample of likely parameter values from a multidimensional distribution, and partial rank correlation coefficients (PRCCs), "a robust sensitivity measure for nonlinear but monotonic relationships between input and output, as long as little to no correlation exists between the inputs", [57][58][59][60] to identify model parameters that have most influence on the threshold R 0 and the COVID-19 transmission. Sensitivity analysis is useful and can help to identify parameters that need to be targeted in designing control strategies.…”

Section: Sensitivity Analysismentioning

confidence: 99%

A fractional order approach to modeling and simulations of the novel COVID-19

Owusu‐Mensah

Akinyemi

Oduro

et al. 2020

Preprint

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The novel coronavirus (SARS-CoV-2.) has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type Susceptible-Exposed-Infected-Recovered (SEIR) model to gain insight into the ongoing pandemic of COVID-19. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution proles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduce the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

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“…e number of research studies that employ mathematical modeling to study the dynamics of infectious disease has rapidly increased over the last two decades. e research foci in this area are ranging from the study of respiratory diseases such as measles, influenza, and tuberculosis; vector-borne diseases such as malaria, Ebola, zikav, and dengue; to sexually transmitted diseases such as HIV/AIDS (see for instance the works of Beay [23], Reynolds et al [24], Mitchell and Ross [25], Egonmwan and Okuonghae [26], Nkamba et al [27], Bakary et al [28], Irwan et al [29], Akgül et al [30], Ainisa et al [31], Carvalho et al [32], Omondi et al [33], and Chong et al [34]). Mathematical modeling is usually used to characterize the epidemiological parameters of disease during outbreaks and to evaluate the effectiveness and schedule of various prevention and control strategies, considering limited resource availability [35].…”

Section: Related Workmentioning

confidence: 99%

Control Policy Mix in Measles Transmission Dynamics Using Vaccination, Therapy, and Treatment

Jaharuddin

Bakhtiar

2020

International Journal of Mathematics and Mathematical Sciences

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This paper considers a deterministic model for the dynamics of measles transmission in a population divided into six classes with respect to the disease states: susceptible, vaccinated, exposed, infected, treated, and recovered. First, we investigate the dynamical properties of the SVEITR model such as its equilibrium points, their stability, and parameter sensitivity by applying constant controls. Criteria for determining the stability of disease-free and endemic equilibrium points are provided in terms of basic reproduction number. The model is then extended by incorporating vaccination, therapy, and treatment rates as time-dependent control variables representing the level of coverages. Application of Pontryagin’s maximum principle provides the necessary conditions that must be satisfied for the existence of optimal controls aiming at minimization of the number of exposed and infected individuals simultaneously with the control effort. Numerical simulations that were carried out using the backward sweep method and Runge–Kutta scheme suggest that optimal controls under moderate and high scenarios can effectively reduce the cases of measles. In particular, the moderate scenario that utilizes the existing coverage level of 86% for MCV1 and 69% for MCV2 can degrade the cost functional by 47% of the low scenario. Meanwhile, high scenario that takes the 2020 target of 96% as coverage only makes a slight difference in reducing the number of exposed and infected individuals.

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Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis

Cited by 46 publications

References 11 publications

A fractional order approach to modeling and simulations of the novel COVID-19

A fractional order approach to modeling and simulations of the novel COVID-19

A fractional order approach to modeling and simulations of the novel COVID-19

Control Policy Mix in Measles Transmission Dynamics Using Vaccination, Therapy, and Treatment

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