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1.
Heliyon ; 8(10): e11195, 2022 Oct.
Article in English | MEDLINE | ID: covidwho-2076136

ABSTRACT

We developed a TB-COVID-19 co-infection epidemic model using a non-linear dynamical system by subdividing the human population into seven compartments. The biological well-posedness of the formulated mathematical model was studied via proving properties like boundedness of solutions, no-negativity, and the solution's dependence on the initial data. We then computed the reproduction numbers separately for TB and COVID-19 sub-models. The criterion for stability conditions for stationary points was examined. The basic reproduction number of sub-models used to suggest the mitigation and persistence of the diseases. Qualitative analysis of the sub-models revealed that the disease-free stationary points are both locally and globally stable provided the respective reproduction numbers are smaller than unit. The endemic stationary points for each sub-models were globally stable if their respective basic reproduction numbers are greater than unit. In each sub-model, we performed an analysis of sensitive parameters concerning the corresponding reproduction numbers. Results from sensitivity indices of the parameters revealed that deceasing contact rate and increasing the transferring rates from the latent stage to an infected class of individuals leads to mitigating the two diseases and their co-infections. We have also studied the analytical behavior of the full co-infection model by deriving the equilibrium points and investigating the conditions of their stability. The numerical experiments of the proposed co-infection model agree with the findings in the analytical results.

2.
Arab Journal of Basic and Applied Sciences ; 29(1):175-192, 2022.
Article in English | Taylor & Francis | ID: covidwho-1882957
3.
Journal of Applied Mathematics ; : 1-20, 2022.
Article in English | Academic Search Complete | ID: covidwho-1765180

ABSTRACT

Tuberculosis (TB) and coronavirus (COVID-19) are both infectious diseases that globally continue affecting millions of people every year. They have similar symptoms such as cough, fever, and difficulty breathing but differ in incubation periods. This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of submodels is also discussed separately after computing the basic reproduction numbers. In each case, the disease-free equilibrium points of the submodels are proved to be both locally and globally stable if the reproduction numbers are less than unity. Besides, the coinfection disease-free equilibrium point is proved to be conditionally stable. The sensitivity and bifurcation analysis are also studied. Different simulation cases were performed to supplement the analytical results. [ FROM AUTHOR] Copyright of Journal of Applied Mathematics is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

4.
Results in Applied Mathematics ; : 100134, 2020.
Article in English | ScienceDirect | ID: covidwho-949717

ABSTRACT

A mathematical model for the transmission dynamics of Coronavirus diseases (COVID-19) is proposed using a system of nonlinear ordinary differential equations by incorporating self protection behavior changes in the population. The disease free equilibrium point is computed, and both the local and global stability analysis was performed. The basic reproduction number (R0) of the model is computed using the method of next generation matrix. The disease free equilibrium point is locally asymptotically and globally stable under certain conditions. Based on the available data, the unknown model parameters are estimated using a combination of least square and Bayesian estimation methods for different countries. The forward sensitivity index is applied to determine and identify the key model parameters for the spread of disease dynamics. The sensitive parameters for the spread of the virus vary from country to country. We found out that the reproduction number depends mostly on the infection rates, the threshold value of the force of infection for a population, the recovery rates, and the virus decay rate in the environment. It illustrates that control of the effective transmission rate (recommended human behavioral change towards self-protective measures) is essential to stop the spreading of the virus. Numerical simulations of the model were performed to supplement and verify the effectiveness of the analytical findings.

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