Mathematics of a sex‐structured model for syphilis transmission dynamics

Gumel, Abba B.; Lubuma, Jean M.‐S.; Sharomi, Oluwaseun; Terefe, Yibeltal Adane

doi:10.1002/mma.4734

Cited by 27 publications

(19 citation statements)

References 52 publications

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“…The public health implication of Theorem 2 is that the spread of the virus can be reduced or controlled when R 0 < 1, if the initial sizes of the sub-populations of the model are in the basin of attraction of the DFE (∇). Global stability of the DFE is necessary to ensure that the disease elimination is independent of the initial sizes of the sub-populations [53].…”

Section: Stability Resultsmentioning

confidence: 99%

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

et al. 2021

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The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

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Section: Stability Resultsmentioning

confidence: 99%

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

et al. 2021

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“…The public health implication of Theorem 4.1 is that COVID-19 can be eliminated or controlled when R 0 < 1, if the initial sizes of the subpopulations of the model are in the basin of attraction of the DFE (∇). Global stability of the DF E is necessary to ensure that the disease elimination is independent of the initial sizes of the subpopulations [50].…”

Section: Stability Results Theorem 41 (Local Stability)mentioning

confidence: 99%

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Iyiola¹,

Oduro²,

Zabilowicz³

et al. 2021

Preprint

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The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalization and deaths have been observed, and thousands of cases daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to understand the transmission of the disease better. Nonlocality involved in the model has made fractional differential equations appropriate for modeling the behavior. However, solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate (from exposed quarantine and recovered to susceptible and infected quarantined individuals), quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium analysis, and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam-Bashforth-Moulton method developed for the fractional order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19, especially quarantining exposed and infected individuals and the effective contact rate. Based on the results with different fractional order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is what is happening right now in many countries.

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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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Mathematics of a sex‐structured model for syphilis transmission dynamics

Cited by 27 publications

References 52 publications

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

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

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