COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

Teklu, Shewafera Wondimagegnhu; Terefe, Birhanu Baye

doi:10.3389/fams.2022.1101029

Cited by 9 publications

(5 citation statements)

References 44 publications

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“…We then follow the approach in [64] to determine the remaining eigenvalues. From the matrix above, the following matrices can be generated as; where;…”

Section: Local Stability Analysis Of Measles-present Equilibriummentioning

confidence: 99%

Modelling the transmission behavior of measles disease considering contaminated environment through a fractal-fractional Mittag-Leffler kernel

Wireko,

Adu,

Gyamfi

et al. 2024

Phys. Scr.

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This work utilises a This work utilises a fractal-fractional operator to examine the dynamics of transmission of measles disease. The existence and uniqueness of the measles model have been thoroughly examined in the context of the fixed point theorem, specifically utilising the Atangana-Baleanu fractal and fractional operators. The model has been demonstrated to possess both \textcolor{blue}{Hyers-Ulam} stability and \textcolor{blue}{Hyers-Ulam Rassias} stability. Furthermore, a qualitative analysis of the model was performed, including examination of key parameters such as the fundamental reproduction number, the \textcolor{blue}{measles}-free and measles-present equilibria, and assessment of global stability. This research has shown that the transmission of \textcolor{blue}{measles} disease is affected by natural phenomena, as changes in the fractal-fractional order lead to changes in the disease dynamics. Furthermore, environmental contamination has been shown to play a significant role in the transmission of the \textcolor{blue}{measles} disease. } fractal-fractional operator to examine the dynamics of transmission of Measles disease. The existence and uniqueness of the Measles model have been thoroughly examined in the context of the fixed point theorem, specifically utilising the Atangana-Baleanu fractal and fractional operators. The model has been demonstrated to possess both hyers ulam stability and hyers lam rassias stability. Furthermore, a qualitative analysis of the model was performed, including examination of key parameters such as the fundamental reproduction number, the Measles-free and Measles-present equilibria, and assessment of global stability. This research has shown that the transmission of Measles disease is affected by natural phenomena, as changes in the fractal-fractional order lead to changes in the disease dynamics. Furthermore, environmental contamination has been shown to play a significant role in the transmission of the Measles disease.

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“…We then follow the approach in [64] to determine the remaining eigenvalues. From the matrix above, the following matrices can be generated as; where;…”

Section: Local Stability Analysis Of Measles-present Equilibriummentioning

confidence: 99%

Modelling the transmission behavior of measles disease considering contaminated environment through a fractal-fractional Mittag-Leffler kernel

Wireko,

Adu,

Gyamfi

et al. 2024

Phys. Scr.

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“…In this section, we provide a thorough qualitative analysis of the time-dependent HIV/AIDS and COVID-19 co-infection model (3). The Pontryagin's Maximum Principle stated in literatures [25,43,51,52,55] is used to describe this analysis, with the aim of minimizing the HIV/ AIDS infection aware individuals denoted by H a , the COVID-19 infected individuals denoted by C i and the total HIV/AIDS and COVID-19 co-infected individuals denoted by M u + M a .…”

Section: Analysis Of the Optimal Control Strategymentioning

confidence: 99%

“…Infectious diseases are diagnostically proven illnesses caused by tiny microorganisms such as viruses, bacteria, fungi, and parasites and have been the leading causes of death throughout the world, for example; viruses cause both COVID-19 and HIV/AIDS infections [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

2023

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HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.

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“…The results show that persistence and eradication depend on intensity magnitude of the white noise as well as parameter values involved in the expansion of the disease. Teklu and Terefe [ 45 ] analyze COVID-19 and syphilis codynamics model to investigate the impacts of intervention measures on the disease transmission. Thangaraj and Easwaramoorthy [ 53 ] investigated a generalized fractal dimension-based comparison of edge detection methods in CT images for estimating the infection of COVID-19 disease.…”

Section: Introductionmentioning

confidence: 99%

Analysis of HBV and COVID‐19 Coinfection Model with Intervention Strategies

Teklu

2023

Computational and Mathematical Methods in Medicine

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Coinfection of hepatitis B virus (HBV) and COVID-19 is a common public health problem throughout some nations in the world. In this study, a mathematical model for hepatitis B virus (HBV) and COVID-19 coinfection is constructed to investigate the effect of protection and treatment mechanisms on its spread in the community. Necessary conditions of the proposed model nonnegativity and boundedness of solutions are analyzed. We calculated the model reproduction numbers and carried out the local stabilities of disease-free equilibrium points whenever the associated reproduction number is less than unity. Using the well-known Castillo-Chavez criteria, the disease-free equilibrium points are shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Sensitivity analysis proved that the most influential parameters are transmission rates. Moreover, we carried out numerical simulation and shown results: some parameters have high spreading effect on the disease transmission, single infections have great impact on the coinfection transmission, and using protections and treatments simultaneously is the most effective strategy to minimize and also to eradicate the HBV and COVID-19 coinfection spreading in the community. It is concluded that to control the transmission of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

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COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

Cited by 9 publications

References 44 publications

Modelling the transmission behavior of measles disease considering contaminated environment through a fractal-fractional Mittag-Leffler kernel

Modelling the transmission behavior of measles disease considering contaminated environment through a fractal-fractional Mittag-Leffler kernel

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

Analysis of HBV and COVID‐19 Coinfection Model with Intervention Strategies

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