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Mathematical Analysis and Sensitivity Assessment of HIV/AIDS-Listeriosis Co-infection Dynamics

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Abstract

Epidemiologically, co-infection is the simultaneous infection of a host by multiple pathogen species such as viruses, bacteria, or fungi. In this work, we model Human Immunodeficiency virus/Acquired Immunodeficiency Syndrome (HIV/AIDS) and Listeriosis co-infection dynamics using a set of nine ordinary differential equations. HIV/AIDS only sub-model and Listeriosis only sub-model are presented and analyzed. The steady states for each sub-model were also determined and the basic reproduction numbers were computed using the next generation matrix approach. The HIV/AIDS only basic reproduction number \(({\mathcal {R}}_{0h})\) and the Listeriosis only infection threshold parameter, \(({\mathcal {R}}_{0l})\) are derived. It has been shown that both the HIV/AIDS-only sub-model and Listeriosis-only sub-model have unique endemic equilibrium. Analysis of the HIV/AIDS-Listeriosis co-infection model is presented and results indicate that the disease-free equilibrium for the HIV/AIDS-Listeriosis co-infection model is globally asymptotically stable. Uncertainty analysis was performed using the Latin Hypercube Sampling Technique and conclusions on the sensitive parameters were drawn. Results from the analysis indicate that to reduce HIV/Listeriosis co-infection there is a need to concentrate on reducing the parameters that bear positive high PRCCs values with P values lower than 0.05. To achieve this there is a need to implement interventions or control measures that reduce the co-infection reproduction number and consequently reduce infection spread within the population. Numerical simulations on the dynamics of the HIV/AIDS-Listeriosis co-infection model are performed and the results support the theoretical findings in the paper. It is envisaged that results obtained from this study will be useful in the fight against HIV/AIDS and Listeriosis co-dynamics.

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Acknowledgements

The authors would like to thank their respective Universities for the production of this paper.

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Authors and Affiliations

  1. Department Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa

    C. W. Chukwu

  2. Department Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa

    M. L. Juga

  3. Department of Decision Sciences, College of Economic and Management Sciences, University of South Africa Preller Street, uckleneuk Ridge, Pretoria, South Africa

    Z. Chazuka

  4. Department of Mathematics, University of Zimbabwe, P.O. Box MP 167, Mount Pleasant, Harare, Zimbabwe

    J. Mushanyu

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  3. Z. Chazuka
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Appendix

Appendix

See Tables 4, 5, 6, 7, 8, 9, 10

Table 4 Table of PRCC significance (for FDR-adjusted P values)
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Table 5 Pairwise PRCC Comparison for FDR-adjusted P values
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Table 6 Pairwise PRCC Comparison for FDR-adjusted P values
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Table 7 Pairwise PRCC Comparison for unadjusted P values for HIV
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Table 8 Pairwise PRCC Comparison for FDR-adjusted P values for HIV
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Table 9 Pairwise PRCC Comparison for unadjusted P values for Listeriosis
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Table 10 Pairwise PRCC Comparison for FDR-adjusted P-values for Listeriosis
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Chukwu, C.W., Juga, M.L., Chazuka, Z. et al. Mathematical Analysis and Sensitivity Assessment of HIV/AIDS-Listeriosis Co-infection Dynamics. Int. J. Appl. Comput. Math 8, 251 (2022). https://doi.org/10.1007/s40819-022-01458-3

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