Search Advanced

Mathematical Biosciences and Engineering

2009, Volume 6, Issue 2: 333-362. doi: 10.3934/mbe.2009.6.333
Previous Article Next Article

Mathematical analysis of a model for HIV-malaria co-infection

  • 1.
    Department of Applied Mathematics, National University of Science and Technology, Box AC 939 Ascot, Bulawayo
  • 2.
    Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2
  • 3.
    Department of Mathematics and Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950
  • 4.
    Mathematics Department, University of Dar es Salaam, P.O.Box 35062, Dar es Salaam
  • Received: 01 December 2007 Accepted: 29 June 2018 Published: 01 March 2009

  • MSC : Primary: 92D30; Secondary: 92B05; 34D23.

  • A deterministic model for the co-interaction of HIV and malaria in a community is presented and rigorously analyzed. Two sub-models, namely the HIV-only and malaria-only sub-models, are considered first of all. Unlike the HIV-only sub-model, which has a globally-asymptotically stable disease-free equilibrium whenever the associated reproduction number is less than unity, the malaria-only sub-model undergoes the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium, for a certain range of the associated reproduction number less than unity. Thus, for malaria, the classical requirement of having the associated reproduction number to be less than unity, although necessary, is not sufficient for its elimination. It is also shown, using centre manifold theory, that the full HIV-malaria co-infection model undergoes backward bifurcation. Simulations of the full HIV-malaria model show that the two diseases co-exist whenever their reproduction numbers exceed unity (with no competitive exclusion occurring). Further, the reduction in sexual activity of individuals with malaria symptoms decreases the number of new cases of HIV and the mixed HIV-malaria infection while increasing the number of malaria cases. Finally, these simulations show that the HIV-induced increase in susceptibility to malaria infection has marginal effect on the new cases of HIV and malaria but increases the number of new cases of the dual HIV-malaria infection.

    Citation: Zindoga Mukandavire, Abba B. Gumel, Winston Garira, Jean Michel Tchuenche. Mathematical analysis of a model for HIV-malaria co-infection[J]. Mathematical Biosciences and Engineering, 2009, 6(2): 333-362. doi: 10.3934/mbe.2009.6.333

    Related Papers:

    [1] Kazeem Oare Okosun, Robert Smith? . Optimal control analysis of malaria-schistosomiasis co-infection dynamics. Mathematical Biosciences and Engineering, 2017, 14(2): 377-405. doi: 10.3934/mbe.2017024
    [2] Churni Gupta, Necibe Tuncer, Maia Martcheva . A network immuno-epidemiological model of HIV and opioid epidemics. Mathematical Biosciences and Engineering, 2023, 20(2): 4040-4068. doi: 10.3934/mbe.2023189
    [3] Nawei Chen, Shenglong Chen, Xiaoyu Li, Zhiming Li . Modelling and analysis of the HIV/AIDS epidemic with fast and slow asymptomatic infections in China from 2008 to 2021. Mathematical Biosciences and Engineering, 2023, 20(12): 20770-20794. doi: 10.3934/mbe.2023919
    [4] Yilong Li, Shigui Ruan, Dongmei Xiao . The Within-Host dynamics of malaria infection with immune response. Mathematical Biosciences and Engineering, 2011, 8(4): 999-1018. doi: 10.3934/mbe.2011.8.999
    [5] Shengqiang Liu, Lin Wang . Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. Mathematical Biosciences and Engineering, 2010, 7(3): 675-685. doi: 10.3934/mbe.2010.7.675
    [6] Pride Duve, Samuel Charles, Justin Munyakazi, Renke Lühken, Peter Witbooi . A mathematical model for malaria disease dynamics with vaccination and infected immigrants. Mathematical Biosciences and Engineering, 2024, 21(1): 1082-1109. doi: 10.3934/mbe.2024045
    [7] Lih-Ing W. Roeger, Z. Feng, Carlos Castillo-Chávez . Modeling TB and HIV co-infections. Mathematical Biosciences and Engineering, 2009, 6(4): 815-837. doi: 10.3934/mbe.2009.6.815
    [8] Qian Ding, Jian Liu, Zhiming Guo . Dynamics of a malaria infection model with time delay. Mathematical Biosciences and Engineering, 2019, 16(5): 4885-4907. doi: 10.3934/mbe.2019246
    [9] Oluwaseun Sharomi, Chandra N. Podder, Abba B. Gumel, Baojun Song . Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment. Mathematical Biosciences and Engineering, 2008, 5(1): 145-174. doi: 10.3934/mbe.2008.5.145
    [10] Churni Gupta, Necibe Tuncer, Maia Martcheva . Immuno-epidemiological co-affection model of HIV infection and opioid addiction. Mathematical Biosciences and Engineering, 2022, 19(4): 3636-3672. doi: 10.3934/mbe.2022168
  • A deterministic model for the co-interaction of HIV and malaria in a community is presented and rigorously analyzed. Two sub-models, namely the HIV-only and malaria-only sub-models, are considered first of all. Unlike the HIV-only sub-model, which has a globally-asymptotically stable disease-free equilibrium whenever the associated reproduction number is less than unity, the malaria-only sub-model undergoes the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium, for a certain range of the associated reproduction number less than unity. Thus, for malaria, the classical requirement of having the associated reproduction number to be less than unity, although necessary, is not sufficient for its elimination. It is also shown, using centre manifold theory, that the full HIV-malaria co-infection model undergoes backward bifurcation. Simulations of the full HIV-malaria model show that the two diseases co-exist whenever their reproduction numbers exceed unity (with no competitive exclusion occurring). Further, the reduction in sexual activity of individuals with malaria symptoms decreases the number of new cases of HIV and the mixed HIV-malaria infection while increasing the number of malaria cases. Finally, these simulations show that the HIV-induced increase in susceptibility to malaria infection has marginal effect on the new cases of HIV and malaria but increases the number of new cases of the dual HIV-malaria infection.


  • This article has been cited by:

    1. K.O. Okosun, O.D. Makinde, A co-infection model of malaria and cholera diseases with optimal control, 2014, 258, 00255564, 19, 10.1016/j.mbs.2014.09.008
    2. Temesgen Awoke, Semu Kassa, Optimal Control Strategy for TB-HIV/AIDS Co-Infection Model in the Presence of Behaviour Modification, 2018, 6, 2227-9717, 48, 10.3390/pr6050048
    3. Farai Nyabadza, Senelani D. Hove-Musekwa, From heroin epidemics to methamphetamine epidemics: Modelling substance abuse in a South African province, 2010, 225, 00255564, 132, 10.1016/j.mbs.2010.03.002
    4. S. Bowong, J. Kurths, Modelling Tuberculosis and Hepatitis B Co-infections, 2010, 5, 0973-5348, 196, 10.1051/mmnp/20105610
    5. Samia Ghersheen, Vladimir Kozlov, Vladimir G. Tkachev, Uno Wennergren, Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity, 2019, 42, 0170-4214, 5805, 10.1002/mma.5671
    6. A. Omame, D. Okuonghae, R.A. Umana, S.C. Inyama, Analysis of a co-infection model for HPV-TB, 2020, 77, 0307904X, 881, 10.1016/j.apm.2019.08.012
    7. Xiulei Jin, Shuwan Jin, Daozhou Gao, Mathematical Analysis of the Ross–Macdonald Model with Quarantine, 2020, 82, 0092-8240, 10.1007/s11538-020-00723-0
    8. Ibrahim M. ELmojtaba, J.Y.T. Mugisha, Mohsin H.A. Hashim, Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan, 2010, 217, 00963003, 2567, 10.1016/j.amc.2010.07.069
    9. O.D. Makinde, K.O. Okosun, Impact of Chemo-therapy on Optimal Control of Malaria Disease with Infected Immigrants, 2011, 104, 03032647, 32, 10.1016/j.biosystems.2010.12.010
    10. Peter Mpasho Mwamtobe, Simphiwe Mpumelelo Simelane, Shirley Abelman, Jean Michel Tchuenche, Optimal control of intervention strategies in malaria–tuberculosis co-infection with relapse, 2018, 11, 1793-5245, 1850017, 10.1142/S1793524518500171
    11. E. Bonyah, M.A. Khan, K.O. Okosun, J.F. Gómez‐Aguilar, On the co‐infection of dengue fever and Zika virus, 2019, 40, 0143-2087, 394, 10.1002/oca.2483
    12. Pierre Magal, Ousmane Seydi, Glenn Webb, Final Size of an Epidemic for a Two-Group SIR Model, 2016, 76, 0036-1399, 2042, 10.1137/16M1065392
    13. N. Hussaini, J. M-S Lubuma, K. Barley, A.B. Gumel, Mathematical analysis of a model for AVL–HIV co-endemicity, 2016, 271, 00255564, 80, 10.1016/j.mbs.2015.10.008
    14. Ayinla Ally Yeketi, Wan Ainun Mior Othman, M. A. Omar Awang, The role of vaccination in curbing tuberculosis epidemic, 2019, 5, 2363-6203, 1689, 10.1007/s40808-019-00623-w
    15. Kazeem O. Okosun, Ouifki Rachid, Nizar Marcus, Optimal control strategies and cost-effectiveness analysis of a malaria model, 2013, 111, 03032647, 83, 10.1016/j.biosystems.2012.09.008
    16. Juan Wang, Xue-Zhi Li, Souvik Bhattacharya, The backward bifurcation of a model for malaria infection, 2018, 11, 1793-5245, 1850018, 10.1142/S1793524518500183
    17. Daozhou Gao, Travis C. Porco, Shigui Ruan, Coinfection dynamics of two diseases in a single host population, 2016, 442, 0022247X, 171, 10.1016/j.jmaa.2016.04.039
    18. KAZEEM OARE OKOSUN, ON THE DYNAMICS MALARIA-DYSENTERY CO-INFECTION MODEL, 2020, 28, 0218-3390, 453, 10.1142/S0218339020400082
    19. Abdon Atangana, Sania Qureshi, 2020, 9781119654223, 225, 10.1002/9781119654223.ch9
    20. Sanaa Moussa Salman, A nonstandard finite difference scheme and optimal control for an HIV model with Beddington–DeAngelis incidence and cure rate, 2020, 135, 2190-5444, 10.1140/epjp/s13360-020-00839-1
    21. K.O. Okosun, Rachid Ouifki, Nizar Marcus, Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity, 2011, 106, 03032647, 136, 10.1016/j.biosystems.2011.07.006
    22. Afshin Babaei, Hossein Jafari, Atena Liya, Mathematical models of HIV/AIDS and drug addiction in prisons, 2020, 135, 2190-5444, 10.1140/epjp/s13360-020-00400-0
    23. K. U. Egeonu, A. Omame, S. C. Inyama, A co-infection model for two-strain Malaria and Cholera with optimal control, 2021, 2195-268X, 10.1007/s40435-020-00748-2
    24. Winston Garira, 2013, Chapter 35, 978-1-4614-4997-3, 595, 10.1007/978-1-4614-4998-0_35
    25. Daozhou Gao, Thomas M. Lietman, Travis C. Porco, Antibiotic resistance as collateral damage: The tragedy of the commons in a two-disease setting, 2015, 263, 00255564, 121, 10.1016/j.mbs.2015.02.007
    26. Lathifah Hanif, Application of optimal control strategies to HIV-malaria co-infection dynamics, 2018, 974, 1742-6588, 012057, 10.1088/1742-6596/974/1/012057
    27. Ana Carvalho, Carla M. A. Pinto, A delay fractional order model for the co-infection of malaria and HIV/AIDS, 2017, 5, 2195-268X, 168, 10.1007/s40435-016-0224-3
    28. Sara Elsheikh, Rachid Ouifki, Kailash C. Patidar, A non-standard finite difference method to solve a model of HIV–Malaria co-infection, 2014, 20, 1023-6198, 354, 10.1080/10236198.2013.821116
    29. Hossein Kheiri, Mohsen Jafari, Optimal control of a fractional-order model for the HIV/AIDS epidemic, 2018, 11, 1793-5245, 1850086, 10.1142/S1793524518500869
    30. C.P. Bhunu, Mathematical analysis of a three-strain tuberculosis transmission model, 2011, 35, 0307904X, 4647, 10.1016/j.apm.2011.03.037
    31. Jemal Mohammed-Awel, Eric Numfor, Optimal insecticide-treated bed-net coverage and malaria treatment in a malaria-HIV co-infection model, 2017, 11, 1751-3758, 160, 10.1080/17513758.2016.1192228
    32. K.O. Okosun, O.D. Makinde, I. Takaidza, Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives, 2013, 37, 0307904X, 3802, 10.1016/j.apm.2012.08.004
    33. A. A. M. Arafa, M. Khalil, A. Sayed, A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay, 2019, 2019, 1076-2787, 1, 10.1155/2019/4291017
    34. Samia Ghersheen, Vladimir Kozlov, Vladimir Tkachev, Uno Wennergren, Mathematical analysis of complex SIR model with coinfection and density dependence, 2019, 1, 2577-7408, 10.1002/cmm4.1042
    35. H. Kheiri, M. Jafari, Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing, 2019, 60, 1598-5865, 387, 10.1007/s12190-018-01219-w
    36. Xiaoming Li, Xianghui Xu, Jie Wang, Jing Li, Sheng Qin, Juxiang Yuan, Study on Prediction Model of HIV Incidence Based on GRU Neural Network Optimized by MHPSO, 2020, 8, 2169-3536, 49574, 10.1109/ACCESS.2020.2979859
    37. ANTTI SOLONEN, HEIKKI HAARIO, JEAN MICHEL TCHUENCHE, HERIETH RWEZAURA, STUDYING THE IDENTIFIABILITY OF EPIDEMIOLOGICAL MODELS USING MCMC, 2013, 06, 1793-5245, 1350008, 10.1142/S1793524513500083
    38. Robert Smith, Kazeem Oare Okosun, Optimal control analysis of malaria–schistosomiasis co-infection dynamics, 2016, 13, 1551-0018, 2, 10.3934/mbe.2017024
    39. Ibrahim M. ELmojtaba, Mathematical model for the dynamics of visceral leishmaniasis-malaria co-infection, 2016, 39, 01704214, 4334, 10.1002/mma.3864
    40. F. Nyabadza, B. T. Bekele, M. A. Rúa, D. M. Malonza, N. Chiduku, M. Kgosimore, The Implications of HIV Treatment on the HIV-Malaria Coinfection Dynamics: A Modeling Perspective, 2015, 2015, 2314-6133, 1, 10.1155/2015/659651
    41. A. Mhlanga, A theoretical model for the transmission dynamics of HIV/HSV-2 co-infection in the presence of poor HSV-2 treatment adherence, 2018, 3, 2444-8656, 603, 10.2478/AMNS.2018.2.00047
    42. Wisdom S. Avusuglo, Kenzu Abdella, Wenying Feng, Stability analysis on an economic epidemiological model with vaccination, 2017, 14, 1551-0018, 975, 10.3934/mbe.2017051
    43. Carla Pinto, Diana Rocha, 2012, A new mathematical model for co-infection of malaria and HIV, 978-1-4673-2703-9, 33, 10.1109/NSC.2012.6304760
    44. Bashir Abdullahi Baba, Bulent Bilgehan, Optimal control of a fractional order model for the COVID – 19 pandemic, 2021, 144, 09600779, 110678, 10.1016/j.chaos.2021.110678
    45. Purity M. Ngina, Rachel Waema Mbogo, Livingstone S. Luboobi, Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells, 2017, 08, 2152-7385, 1153, 10.4236/am.2017.88087
    46. Sandeep Sharma, Nitu Kumari, 2018, Chapter 51, 978-981-10-5328-3, 673, 10.1007/978-981-10-5329-0_51
    47. K. O. Okosun, M. A. Khan, E. Bonyah, S. T. Ogunlade, On the dynamics of HIV-AIDS and cryptosporidiosis, 2017, 132, 2190-5444, 10.1140/epjp/i2017-11625-3
    48. Peter M. Mwamtobe, Shirley Abelman, J. Michel Tchuenche, Ansley Kasambara, Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi, 2014, 2014, 1085-3375, 1, 10.1155/2014/594256
    49. Baba Seidu, Oluwole D. Makinde, Ibrahim Y. Seini, Mathematical Analysis of the Effects of HIV-Malaria Co-infection on Workplace Productivity, 2015, 63, 0001-5342, 151, 10.1007/s10441-015-9255-y
    50. E. Lungu, T. J. Massaro, E. Ndelwa, N. Ainea, S. Chibaya, N. J. Malunguza, Mathematical Modeling of the HIV/Kaposi’s Sarcoma Coinfection Dynamics in Areas of High HIV Prevalence, 2013, 2013, 1748-670X, 1, 10.1155/2013/753424
    51. S. Mushayabasa, J.M. Tchuenche, C.P. Bhunu, E. Ngarakana-Gwasira, Modeling gonorrhea and HIV co-interaction, 2011, 103, 03032647, 27, 10.1016/j.biosystems.2010.09.008
    52. Oluwatayo M. Ogunmiloro, Local and global asymptotic behavior of malaria-filariasis coinfections in compliant and noncompliant susceptible pregnant women to antenatal medical program in the tropics, 2019, 2019, 2544-9990, 31, 10.2478/ejaam-2019-0003
    53. Oluwatayo M. Ogunmiloro, Mathematical Modeling of the Coinfection Dynamics of Malaria-Toxoplasmosis in the Tropics, 2019, 56, 1896-3811, 139, 10.2478/bile-2019-0013
    54. M.S. Goudiaby, L.D. Gning, M.L. Diagne, Ben M. Dia, H. Rwezaura, J.M. Tchuenche, Optimal control analysis of a COVID-19 and tuberculosis co-dynamics model, 2022, 28, 23529148, 100849, 10.1016/j.imu.2022.100849
    55. Anwarud Din, Saida Amine, Amina Allali, A stochastically perturbed co-infection epidemic model for COVID-19 and hepatitis B virus, 2023, 111, 0924-090X, 1921, 10.1007/s11071-022-07899-1
    56. Zinabu Teka Melese, Haileyesus Tessema Alemneh, Enhancing reservoir control in the co-dynamics of HIV-VL: from mathematical modeling perspective, 2021, 2021, 1687-1847, 10.1186/s13662-021-03584-6
    57. Hilda Fahlena, Rudy Kusdiantara, Nuning Nuraini, Edy Soewono, Dynamical analysis of two-pathogen coinfection in influenza and other respiratory diseases, 2022, 155, 09600779, 111727, 10.1016/j.chaos.2021.111727
    58. Solomon Kadaleka, Shirley Abelman, Jean M. Tchuenche, A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding, 2021, 69, 0001-5342, 511, 10.1007/s10441-021-09416-0
    59. A. Omame, H. Rwezaura, M. L. Diagne, S. C. Inyama, J. M. Tchuenche, COVID-19 and dengue co-infection in Brazil: optimal control and cost-effectiveness analysis, 2021, 136, 2190-5444, 10.1140/epjp/s13360-021-02030-6
    60. M.L. Diagne, H. Rwezaura, S.A. Pedro, J.M. Tchuenche, Theoretical analysis of a measles model with nonlinear incidence functions, 2023, 117, 10075704, 106911, 10.1016/j.cnsns.2022.106911
    61. HUSSAM ALRABAIAH, MATI UR RAHMAN, IBRAHIM MAHARIQ, SAMIA BUSHNAQ, MUHAMMAD ARFAN, FRACTIONAL ORDER ANALYSIS OF HBV AND HCV CO-INFECTION UNDER ABC DERIVATIVE, 2022, 30, 0218-348X, 10.1142/S0218348X22400369
    62. Scott Greenhalgh, Carly Rozins, A generalized differential equation compartmental model of infectious disease transmission, 2021, 6, 24680427, 1073, 10.1016/j.idm.2021.08.007
    63. M. L. Diagne, H. Rwezaura, S. Y. Tchoumi, J. M. Tchuenche, Jan Rychtar, A Mathematical Model of COVID-19 with Vaccination and Treatment, 2021, 2021, 1748-6718, 1, 10.1155/2021/1250129
    64. S.Y. Tchoumi, E.Z. Dongmo, J.C. Kamgang, J.M. Tchuenche, Dynamics of a two-group structured malaria transmission model, 2022, 29, 23529148, 100897, 10.1016/j.imu.2022.100897
    65. Wei-Yun Shen, Yu-Ming Chu, Mati ur Rahman, Ibrahim Mahariq, Anwar Zeb, Mathematical analysis of HBV and HCV co-infection model under nonsingular fractional order derivative, 2021, 28, 22113797, 104582, 10.1016/j.rinp.2021.104582
    66. S.Y. Tchoumi, H. Rwezaura, J.M. Tchuenche, Dynamic of a two-strain COVID-19 model with vaccination, 2022, 39, 22113797, 105777, 10.1016/j.rinp.2022.105777
    67. Bevina D. Handari, Rossi A. Ramadhani, Chidozie W. Chukwu, Sarbaz H. A. Khoshnaw, Dipo Aldila, An Optimal Control Model to Understand the Potential Impact of the New Vaccine and Transmission-Blocking Drugs for Malaria: A Case Study in Papua and West Papua, Indonesia, 2022, 10, 2076-393X, 1174, 10.3390/vaccines10081174
    68. S.Y. Tchoumi, M.L. Diagne, H. Rwezaura, J.M. Tchuenche, Malaria and COVID-19 co-dynamics: A mathematical model and optimal control, 2021, 99, 0307904X, 294, 10.1016/j.apm.2021.06.016
    69. N. Ringa, M.L. Diagne, H. Rwezaura, A. Omame, S.Y. Tchoumi, J.M. Tchuenche, HIV and COVID-19 co-infection: A mathematical model and optimal control, 2022, 31, 23529148, 100978, 10.1016/j.imu.2022.100978
    70. Solomon Kadaleka, Shirley Abelman, Jean M. Tchuenche, A Mathematical Model of the Transmission Dynamics of Bovine Schistosomiasis with Contaminated Environment, 2022, 70, 0001-5342, 10.1007/s10441-021-09434-y
    71. Baba Seidu, Oluwole Daniel Makinde, Ibrahim Yakubu Seini, Andrew Pickering, On the Optimal Control of HIV-TB Co-Infection and Improvement of Workplace Productivity, 2023, 2023, 1607-887X, 1, 10.1155/2023/3716235
    72. Mamadou Lamine Diagne, Herieth Rwezaura, S.A. Pedro, Jean Michel Tchuenche, Theoretical Analysis of a Measles Model with Nonlinear Incidence Functions, 2022, 1556-5068, 10.2139/ssrn.4160579
    73. Sanaa Moussa Salman, Strong Resonance Bifurcations in a Discrete-Time In-Host Model With a Saturating Infection Rate, 2023, 18, 1555-1415, 10.1115/1.4062390
    74. Dereje Gutema Edossa, Alemu Geleta Wedajo, Purnachandra Rao Koya, Andrei Korobeinikov, Optimal Combinations of Control Strategies and Cost-Effectiveness Analysis of Dynamics of Endemic Malaria Transmission Model, 2023, 2023, 1748-6718, 1, 10.1155/2023/7677951
    75. I. Ratti, P. Kalra, Study of Disease Dynamics of Co-infection of Rotavirus and Malaria with Control Strategies, 2023, 17, 1823-8343, 151, 10.47836/mjms.17.2.05
    76. Abou Bakari Diabaté, Boureima Sangaré, Ousmane Koutou, Optimal control analysis of a COVID-19 and Tuberculosis (TB) co-infection model with an imperfect vaccine for COVID-19, 2023, 2254-3902, 10.1007/s40324-023-00330-8
    77. Adesoye Idowu Abioye, Olumuyiwa James Peter, Hammed Abiodun Ogunseye, Festus Abiodun Oguntolu, Tawakalt Abosede Ayoola, Asimiyu Olalekan Oladapo, A fractional-order mathematical model for malaria and COVID-19 co-infection dynamics, 2023, 27724425, 100210, 10.1016/j.health.2023.100210
    78. Zhenfeng Shi, Daqing Jiang, A viral co-infection model with general infection rate in deterministic and stochastic environments, 2023, 10075704, 107436, 10.1016/j.cnsns.2023.107436
    79. Zenebe Shiferaw Kifle, Legesse Lemecha Obsu, Mathematical modeling and analysis of COVID-19 and TB co-dynamics, 2023, 9, 24058440, e18726, 10.1016/j.heliyon.2023.e18726
    80. Alina Glaubitz, Feng Fu, Population heterogeneity in vaccine coverage impacts epidemic thresholds and bifurcation dynamics, 2023, 24058440, e19094, 10.1016/j.heliyon.2023.e19094
    81. Simeon Adeyemo, Adekunle Sangotola, Olga Korosteleva, Modeling Transmission Dynamics of Tuberculosis–HIV Co-Infection in South Africa, 2023, 4, 2673-3986, 408, 10.3390/epidemiologia4040036
    82. Sonu Chugh, Joydip Dhar, Rangan K. Guha, Stability and optimal control of two products innovation diffusion system, 2023, 26667207, 100344, 10.1016/j.rico.2023.100344
    83. Folashade B. Agusto, Ramsès Djidjou-Demasse, Ousmane Seydi, Mathematical model of Ehrlichia chaffeensis transmission dynamics in dogs , 2023, 17, 1751-3758, 10.1080/17513758.2023.2287082
    84. Shaima Al-Shanfari, Ibrahim M. Elmojtaba, Nasser Al-Salti, Fatima Al-Shandari, Mathematical analysis and optimal control of cholera-malaria co-infection model, 2024, 26667207, 100393, 10.1016/j.rico.2024.100393
    85. C.W. Chukwu, S.Y. Tchoumi, M.L. Diagne, A simulation study to assess the epidemiological impact of pneumonia transmission dynamics in high-risk populations, 2024, 10, 27726622, 100423, 10.1016/j.dajour.2024.100423
    86. Naresh Kumar Jothi, A. Lakshmi, 2024, Chapter 43, 978-981-99-8645-3, 551, 10.1007/978-981-99-8646-0_43
    87. Oluwatayo Michael Ogunmiloro, Amos Sesan Idowu, Dynamic insights into malaria–onchocerciasis co-disease transmission: mathematical modeling, basic reproduction number and sensitivity analysis, 2024, 30, 1405-213X, 10.1007/s40590-024-00601-y
    88. Rasha Majeed Yaseen, Hassan Fadhil Al-Husseiny, 2024, 3061, 0094-243X, 040040, 10.1063/5.0196252
    89. Afonso Dimas Martins, Mick Roberts, Quirine ten Bosch, Hans Heesterbeek, Indirect interaction between an endemic and an invading pathogen: A case study of Plasmodium and Usutu virus dynamics in a shared bird host population, 2024, 157, 00405809, 118, 10.1016/j.tpb.2024.04.002
    90. J. O. Akanni, S. Ajao, S. F. Abimbade, , Dynamical analysis of COVID-19 and tuberculosis co-infection using mathematical modelling approach, 2024, 4, 2767-8946, 208, 10.3934/mmc.2024018
    91. Michael Byamukama, Damian Kajunguri, Martin Karuhanga, Optimal control analysis of pneumonia and HIV/AIDS co-infection model, 2024, 03, 2811-0072, 10.1142/S2811007224500068
    92. M.G. Roberts, Infection thresholds for two interacting pathogens in a wild animal population, 2024, 375, 00255564, 109258, 10.1016/j.mbs.2024.109258
    93. Akeem Olarewaju Yunus, Morufu Oyedunsi Olayiwola, Mathematical modeling of malaria epidemic dynamics with enlightenment and therapy intervention using the Laplace-Adomian decomposition method and Caputo fractional order, 2024, 8, 27731863, 100147, 10.1016/j.fraope.2024.100147
    94. Yaxin Ren, Yakui Xue, Modeling and optimal control of COVID-19 and malaria co-infection based on vaccination, 2024, 4, 2767-8946, 316, 10.3934/mmc.2024026
    95. Philip N. A. Akuka, Baba Seidu, Eric Okyere, Stephen Abagna, Mohamed Abdelsalam, Fractional‐Order Epidemic Model for Measles Infection, 2024, 2024, 2090-908X, 10.1155/2024/8997302
    96. Nouar Chorfi, Samir Bendoukha, Salem Abdelmalek, The optimal control of an HIV/AIDS reaction-diffusion epidemic model, 2024, 0, 1937-1632, 0, 10.3934/dcdss.2024193
    97. Kshama Jain, Anuradha Bhattacharjee, Srikumar Krishnamurhty, Mathematical analysis of COVID-19 and TB co-infection dynamics with optimal control, 2025, 11, 2363-6203, 10.1007/s40808-024-02197-8
    98. Jamal Shah, Hameed Khan, Emad A. A. Ismail, Fuad A. Awaad, Abhinav Kumar, Modeling scabies transmission dynamics: a stochastic approach with spectral collocation and neural network insights, 2025, 140, 2190-5444, 10.1140/epjp/s13360-025-06025-5
    99. Michael Byamukama, Martin Karuhanga, Damian Kajunguri, Nian-Sheng Tang, Mathematical Analysis of the Role of Treatment and Vaccination in the Management of the HIV/AIDS and Pneumococcal Pneumonia Co‐Infection, 2025, 2025, 2314-4629, 10.1155/jom/5879698
    100. Anum Aish Buhader, Mujahid Abbas, Mudassar Imran, Andrew Omame, Existence and stability results in a fractional optimal control model for dengue and two-strains of salmonella typhi, 2025, 13, 26668181, 101075, 10.1016/j.padiff.2025.101075
    101. Purnendu Sardar, Santosh Biswas, Krishna Pada Das, Saroj Kumar Sahani, Vikas Gupta, Stability, sensitivity, and bifurcation analysis of a fractional-order HIV model of CD
    4+
    T cells with memory and external virus transmission from macrophages, 2025, 140, 2190-5444, 10.1140/epjp/s13360-025-06081-x
    102. Shikha Saha, Amit Kumar Saha, Chandra Nath Podder, Dynamics of COVID-malaria co-infection with optimal control and cost-effectiveness analysis, 2025, 14, 26668181, 101217, 10.1016/j.padiff.2025.101217
  • Reader Comments
  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(4589) PDF downloads(831) Cited by(102)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog