Modeling and Optimizing Multi-Faceted Strategies for HPV Control: Insights from a Nonlinear Mathematical Approach
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Published:
Sep 30, 2023
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Keywords:
HPV Dynamics, Optimal Control Strategies, Mathematical Modeling, Disease Prevention, Public Health Interventions
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Abstract
This study presents a nonlinear deterministic mathematical model of Human Papillomavirus (HPV) dynamics, emphasizing qualitative analysis through the stability theory of differential equations. Our investigation focuses on validating the existence and stability of disease-free and endemic equilibrium points using the basic reproduction number governing HPV transmission. Notably, the model exhibits a backward bifurcation, prompting a sensitivity analysis. We address the challenge of HPV control by formulating an optimal control problem, applying the Pontryagin maximum principle with three distinct strategies: prevention, treatment, and screening. Numerical simulations reveal that a combined approach involving prevention, screening, and treatment emerges as the most effective strategy for eradicating HPV within the community. In conclusion, this study offers a comprehensive mathematical model for HPV dynamics and underscores the importance of multi-faceted intervention strategies. Our findings have significant implications for public health initiatives aiming to combat HPV infections and reduce their impact on communities.
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How to Cite
[1]
G. Rusmayadi, A. D. W. Muhammad Sidik, H. Lumbantobing, B. Indrawan, E. Edwinanto, and Y. Imamulhak, “Modeling and Optimizing Multi-Faceted Strategies for HPV Control: Insights from a Nonlinear Mathematical Approach”, Fidelity, vol. 5, no. 3, pp. 239-253, Sep. 2023.
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Received 2023-07-20
Accepted 2023-09-15
Published 2023-09-30
Accepted 2023-09-15
Published 2023-09-30
References
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Powell, S. E., Hariri, S., Steinau, M., Bauer, H. M., Bennett, N. M., Bloch, K. C., ... & Markowitz, L. E. (2012). Impact of human papillomavirus (HPV) vaccination on HPV 16/18-related prevalence in precancerous cervical lesions. Vaccine, 31(1), 109-113.
Rajandran, P. Post licensure surveillance of Human Papillomavirus vaccine, vaccine adverse event reporting system, 2010-2017 (Doctoral dissertation, University of Nottingham).
Battaglia, F., Plotti, F., Zullo, M. A., Panici, P. B., Plotti, G., Brown, L. A., ... & Chia, S. (2006). Gynecologic cancer. Cancer, 16, 29-35.
Sharma, S. (2022). Development of Microfluidic Platform for Infectious Disease Diagnosis and Sperm Cell Sorting (Doctoral dissertation, Florida Atlantic University).
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Machalek, D. A., Roberts, J. M., Garland, S. M., Thurloe, J., Richards, A., Chambers, I., ... & Farnsworth, A. (2019). Routine cervical screening by primary HPV testing: early findings in the renewed National Cervical Screening Program. Medical Journal of Australia, 211(3), 113-119.
Sankaranarayanan, R., Prabhu, P. R., Pawlita, M., Gheit, T., Bhatla, N., Muwonge, R., ... & Pillai, M. R. (2016). Immunogenicity and HPV infection after one, two, and three doses of quadrivalent HPV vaccine in girls in India: a multicentre prospective cohort study. The lancet oncology, 17(1), 67-77.
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Gurmu, E. D., & Koya, P. R. (2019). Impact of chemotherapy treatment of SITR compartmentalization and modeling of human papilloma virus (HPV). IOSR Journal of Mathematics (IOSR–JM), 15(3), 17-29.
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Lumbantobing, H., Sidik, A. D. W., Junfithrana, A. P., Suryana, A., Tambunan, H. B., Yudono, M. A. S., ... & Imamulhak, Y. (2023). Contribution of Disaster Response Team in Assisting Natural Disaster Mitigation in Cianjur. Jurnal Pengabdian dan Pemberdayaan Masyarakat Indonesia, 3(8), 406-417.
Efendi, E., Muslim, A. I., & Sidik, A. D. W. M. (2023). Design and Analysis of Grid Connected Photovoltaic Rooftop System in Emergency Room (IGD) Regional General Hospital (RSUD) Hj. Anna Lasmanah Banjarnegara. Fidelity: Jurnal Teknik Elektro, 5(1), 18-27.
Indrawan, B., Sidik, A. D. W. M., Junfithrana, A. P., Artiyasa, M., Kusumah, I. H., & Kurniawan, A. (2023). Design of Solar Rooftop Using Helioscope in The Gazebo of Pelabuhan Ratu Coal Power Plant. Fidelity: Jurnal Teknik Elektro, 5(1), 28-34.
Sidik, A., Lumbantobing, H., Suryana, A., Yudono, M. A. S., Putra, Y., Imamulhak, Y., & Indrawan, B. (2022). EEG-Based Classification of Schizophrenia and Bipolar Disorder with the Fuzzy Method. INTERNATIONAL JOURNAL ENGINEERING AND APPLIED TECHNOLOGY (IJEAT), 5(2), 1-6.
Arsyad, M., Geraldi, R., Sidik, A. D. W. M., Kusumah, I. H., Artiyasa, M., & Junfithrana, A. P. (2022, July). Study of Solar Photovoltaic Rooftop System for 1300 VA Residential Load Connected to Grid in Sukabumi. In 2022 IEEE 8th International Conference on Computing, Engineering and Design (ICCED) (pp. 1-5). IEEE.
Dharmawan, D. M., Akbar, H. I., Maulana, R., Sidik, A. D. W. M., Kusumah, I. H., & Artiyasa, M. (2022, July). Analysis of Grid-Connected Solar Photovoltaic Rooftop System for 900 VA Residential Load in Sukabumi. In 2022 IEEE 8th International Conference on Computing, Engineering and Design (ICCED) (pp. 1-5). IEEE.
Yudono, M. A. S., Sidik, A. D. W. M., Kusumah, I. H., Suryana, A., Junfithrana, A. P., Nugraha, A., ... & Imamulhak, Y. (2022). Bitcoin USD Closing Price (BTC-USD) Comparison Using Simple Moving Average And Radial Basis Function Neural Network Methods. FIDELITY: Jurnal Teknik Elektro, 4(2), 29-34.
Yudono, M. A. S., Faris, R. M., De Wibowo, A., Sidik, M., Sembiring, F., & Aji, S. F. (2022, February). Fuzzy Decision Support System for ABC University Student Admission Selection. In International Conference on Economics, Management and Accounting (ICEMAC 2021) (pp. 230-237). Atlantis Press.
Sidik, A. D. W. M. (2022). Design and Implementation of Food Crop Technology Using PLC and IoT. Prosiding Icontention, 1.
Sidik, A. D. W. M., & Akbar, Z. (2021). Analyzing the Potential for Utilization of New Renewable Energy to Support the Electricity System in the Cianjur Regency Region. Fidelity: Jurnal Teknik Elektro, 3(3), 46-51.
Suryana, A., Junfithrana, A. P., Kusumah, I. H., De Wibowo, A., Artiyasa, M., Imamulhak, Y., & Putra, Y. (2020). Automatic Gas Control System In The Motorcycle Braking Process With The Concept Of Non-Uniform Slowing Down Motion. FIDELITY: Jurnal Teknik Elektro, 2(3), 51-56.
Artiyasa, M., Kusumah, I. H., Suryana, A., Sidik, A. D. W. M., & Junfithrana, A. P. (2020). Comparative Study of Internet of Things (IoT) Platform for Smart Home Lighting Control Using NodeMCU with Thingspeak and Blynk Web Applications. FIDELITY: Jurnal Teknik Elektro, 2(1), 1-6.
Maulana, R., & Sidik, A. D. W. M. (2019). Design of an Automatic Nutrition System for Hydroponic Plants with an IoT-based NodeMCU Microcontroller. FIDELITY: Jurnal Teknik Elektro, 1(2), 1-5.
Brisson, M., Kim, J. J., Canfell, K., Drolet, M., Gingras, G., Burger, E. A., ... & Hutubessy, R. (2020). Impact of HPV vaccination and cervical screening on cervical cancer elimination: a comparative modelling analysis in 78 low-income and lower-middle-income countries. The Lancet, 395(10224), 575-590.
Drolet, M., Bénard, É., Pérez, N., Brisson, M., Ali, H., Boily, M. C., ... & Yu, B. N. (2019). Population-level impact and herd effects following the introduction of human papillomavirus vaccination programmes: updated systematic review and meta-analysis. The Lancet, 394(10197), 497-509.
Jit, M., Brisson, M., Portnoy, A., & Hutubessy, R. (2014). Cost-effectiveness of female human papillomavirus vaccination in 179 countries: a PRIME modelling study. The Lancet Global health, 2(7), e406-e414.
Lei, J., Ploner, A., Elfström, K. M., Wang, J., Roth, A., Fang, F., ... & Sparén, P. (2020). HPV vaccination and the risk of invasive cervical cancer. New England Journal of Medicine, 383(14), 1340-1348.
Mishra, G. A., Pimple, S. A., & Shastri, S. S. (2011). An overview of prevention and early detection of cervical cancers. Indian Journal of Medical and Paediatric Oncology, 32(03), 125-132.
Powell, S. E., Hariri, S., Steinau, M., Bauer, H. M., Bennett, N. M., Bloch, K. C., ... & Markowitz, L. E. (2012). Impact of human papillomavirus (HPV) vaccination on HPV 16/18-related prevalence in precancerous cervical lesions. Vaccine, 31(1), 109-113.
Rajandran, P. Post licensure surveillance of Human Papillomavirus vaccine, vaccine adverse event reporting system, 2010-2017 (Doctoral dissertation, University of Nottingham).
Battaglia, F., Plotti, F., Zullo, M. A., Panici, P. B., Plotti, G., Brown, L. A., ... & Chia, S. (2006). Gynecologic cancer. Cancer, 16, 29-35.
Sharma, S. (2022). Development of Microfluidic Platform for Infectious Disease Diagnosis and Sperm Cell Sorting (Doctoral dissertation, Florida Atlantic University).
Garland, S. M., Kjaer, S. K., Muñoz, N., Block, S. L., Brown, D. R., DiNubile, M. J., ... & Velicer, C. (2016). Impact and effectiveness of the quadrivalent human papillomavirus vaccine: a systematic review of 10 years of real-world experience. Reviews of Infectious Diseases, 63(4), 519-527.
Herrero, R., Quint, W., Hildesheim, A., Gonzalez, P., Struijk, L., Katki, H. A., ... & CVT Vaccine Group. (2013). Reduced prevalence of oral human papillomavirus (HPV) 4 years after bivalent HPV vaccination in a randomized clinical trial in Costa Rica. PloS one, 8(7), e68329.
Sawaya, G. F., Sanstead, E., Alarid-Escudero, F., Smith-McCune, K., Gregorich, S. E., Silverberg, M. J., ... & Kulasingam, S. (2019). Estimated quality of life and economic outcomes associated with 12 cervical cancer screening strategies: a cost-effectiveness analysis. JAMA internal medicine, 179(7), 867-878.
Machalek, D. A., Roberts, J. M., Garland, S. M., Thurloe, J., Richards, A., Chambers, I., ... & Farnsworth, A. (2019). Routine cervical screening by primary HPV testing: early findings in the renewed National Cervical Screening Program. Medical Journal of Australia, 211(3), 113-119.
Sankaranarayanan, R., Prabhu, P. R., Pawlita, M., Gheit, T., Bhatla, N., Muwonge, R., ... & Pillai, M. R. (2016). Immunogenicity and HPV infection after one, two, and three doses of quadrivalent HPV vaccine in girls in India: a multicentre prospective cohort study. The lancet oncology, 17(1), 67-77.
Giannone, G., Giuliano, A. R., Bandini, M., Marandino, L., Raggi, D., Earle, W., ... & Necchi, A. (2022). HPV vaccination and HPV-related malignancies: impact, strategies and optimizations toward global immunization coverage. Cancer treatment reviews, 102467.
Gurmu, E. D., & Koya, P. R. (2019). Impact of chemotherapy treatment of SITR compartmentalization and modeling of human papilloma virus (HPV). IOSR Journal of Mathematics (IOSR–JM), 15(3), 17-29.
Gurmu, E. D., & Koya, P. R. (2019). Sensitivity analysis and modeling the impact of screening on the transmission dynamics of human papilloma virus (HPV). American journal of applied mathematics, 7(3), 70-79.
Taberna, M., Mena, M., Pavón, M. A., Alemany, L., Gillison, M. L., & Mesía, R. (2017). Human papillomavirus-related oropharyngeal cancer. Annals of Oncology, 28(10), 2386-2398.
Lumbantobing, H., Sidik, A. D. W., Junfithrana, A. P., Suryana, A., Tambunan, H. B., Yudono, M. A. S., ... & Imamulhak, Y. (2023). Contribution of Disaster Response Team in Assisting Natural Disaster Mitigation in Cianjur. Jurnal Pengabdian dan Pemberdayaan Masyarakat Indonesia, 3(8), 406-417.
Efendi, E., Muslim, A. I., & Sidik, A. D. W. M. (2023). Design and Analysis of Grid Connected Photovoltaic Rooftop System in Emergency Room (IGD) Regional General Hospital (RSUD) Hj. Anna Lasmanah Banjarnegara. Fidelity: Jurnal Teknik Elektro, 5(1), 18-27.
Indrawan, B., Sidik, A. D. W. M., Junfithrana, A. P., Artiyasa, M., Kusumah, I. H., & Kurniawan, A. (2023). Design of Solar Rooftop Using Helioscope in The Gazebo of Pelabuhan Ratu Coal Power Plant. Fidelity: Jurnal Teknik Elektro, 5(1), 28-34.
Sidik, A., Lumbantobing, H., Suryana, A., Yudono, M. A. S., Putra, Y., Imamulhak, Y., & Indrawan, B. (2022). EEG-Based Classification of Schizophrenia and Bipolar Disorder with the Fuzzy Method. INTERNATIONAL JOURNAL ENGINEERING AND APPLIED TECHNOLOGY (IJEAT), 5(2), 1-6.
Arsyad, M., Geraldi, R., Sidik, A. D. W. M., Kusumah, I. H., Artiyasa, M., & Junfithrana, A. P. (2022, July). Study of Solar Photovoltaic Rooftop System for 1300 VA Residential Load Connected to Grid in Sukabumi. In 2022 IEEE 8th International Conference on Computing, Engineering and Design (ICCED) (pp. 1-5). IEEE.
Dharmawan, D. M., Akbar, H. I., Maulana, R., Sidik, A. D. W. M., Kusumah, I. H., & Artiyasa, M. (2022, July). Analysis of Grid-Connected Solar Photovoltaic Rooftop System for 900 VA Residential Load in Sukabumi. In 2022 IEEE 8th International Conference on Computing, Engineering and Design (ICCED) (pp. 1-5). IEEE.
Yudono, M. A. S., Sidik, A. D. W. M., Kusumah, I. H., Suryana, A., Junfithrana, A. P., Nugraha, A., ... & Imamulhak, Y. (2022). Bitcoin USD Closing Price (BTC-USD) Comparison Using Simple Moving Average And Radial Basis Function Neural Network Methods. FIDELITY: Jurnal Teknik Elektro, 4(2), 29-34.
Yudono, M. A. S., Faris, R. M., De Wibowo, A., Sidik, M., Sembiring, F., & Aji, S. F. (2022, February). Fuzzy Decision Support System for ABC University Student Admission Selection. In International Conference on Economics, Management and Accounting (ICEMAC 2021) (pp. 230-237). Atlantis Press.
Sidik, A. D. W. M. (2022). Design and Implementation of Food Crop Technology Using PLC and IoT. Prosiding Icontention, 1.
Sidik, A. D. W. M., & Akbar, Z. (2021). Analyzing the Potential for Utilization of New Renewable Energy to Support the Electricity System in the Cianjur Regency Region. Fidelity: Jurnal Teknik Elektro, 3(3), 46-51.
Suryana, A., Junfithrana, A. P., Kusumah, I. H., De Wibowo, A., Artiyasa, M., Imamulhak, Y., & Putra, Y. (2020). Automatic Gas Control System In The Motorcycle Braking Process With The Concept Of Non-Uniform Slowing Down Motion. FIDELITY: Jurnal Teknik Elektro, 2(3), 51-56.
Artiyasa, M., Kusumah, I. H., Suryana, A., Sidik, A. D. W. M., & Junfithrana, A. P. (2020). Comparative Study of Internet of Things (IoT) Platform for Smart Home Lighting Control Using NodeMCU with Thingspeak and Blynk Web Applications. FIDELITY: Jurnal Teknik Elektro, 2(1), 1-6.
Maulana, R., & Sidik, A. D. W. M. (2019). Design of an Automatic Nutrition System for Hydroponic Plants with an IoT-based NodeMCU Microcontroller. FIDELITY: Jurnal Teknik Elektro, 1(2), 1-5.