Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis
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,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-10-01
|
| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844022024835 |
| _version_ | 1797991726833467392 |
|---|---|
| author | Kassahun Getnet Mekonen Legesse Lemecha Obsu |
| author_facet | Kassahun Getnet Mekonen Legesse Lemecha Obsu |
| author_sort | Kassahun Getnet Mekonen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T08:56:29Z |
| format | Article |
| id | doaj.art-731e942d7183471c91be4df230ec1211 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-11T08:56:29Z |
| publishDate | 2022-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-731e942d7183471c91be4df230ec12112022-12-22T04:33:17ZengElsevierHeliyon2405-84402022-10-01810e11195Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosisKassahun Getnet Mekonen0Legesse Lemecha Obsu1Department of Mathematics, Hawassa University, Hawassa, Ethiopia; Corresponding author.Department of Applied Mathematics, Adama Science and Technology University, Adama, EthiopiaWe 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.http://www.sciencedirect.com/science/article/pii/S2405844022024835TBCOVID-19Co-infectionStability analysisSensitivity |
| spellingShingle | Kassahun Getnet Mekonen Legesse Lemecha Obsu Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis Heliyon TB COVID-19 Co-infection Stability analysis Sensitivity |
| title | Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis |
| title_full | Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis |
| title_fullStr | Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis |
| title_full_unstemmed | Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis |
| title_short | Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis |
| title_sort | mathematical modeling and analysis for the co infection of covid 19 and tuberculosis |
| topic | TB COVID-19 Co-infection Stability analysis Sensitivity |
| url | http://www.sciencedirect.com/science/article/pii/S2405844022024835 |
| work_keys_str_mv | AT kassahungetnetmekonen mathematicalmodelingandanalysisforthecoinfectionofcovid19andtuberculosis AT legesselemechaobsu mathematicalmodelingandanalysisforthecoinfectionofcovid19andtuberculosis |