Mathematical modeling and optimal control of HPV-related cervical cancer through awareness campaigns and vaccination

Khalid Aldawsari; Fahad Al Basir; Khalid Aldawsari; Fahad Al Basir

doi:10.3934/nhm.2026046

Networks and Heterogeneous Media

2026, Volume 21, Issue 4: 1146-1171. doi: 10.3934/nhm.2026046

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Mathematical modeling and optimal control of HPV-related cervical cancer through awareness campaigns and vaccination

Khalid Aldawsari ^{1
,
,},
Fahad Al Basir ^{2
,
,}

1.
Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
2.
Department of Mathematics, Asansol Girls' College, Asansol-4, West Bengal 713304, India

Received: 13 February 2026 Revised: 23 April 2026 Accepted: 07 May 2026 Published: 02 June 2026

In this research, we have derived a mathematical model to study the impact of health center-based awareness campaigns on the spread of human papillomavirus (HPV) infection to cervical cancer. In the model, the human population is divided into susceptible, vaccinated, permanently immune, infected with HPV, and recovered. Moreover, awareness level is assumed as a model compartment. The awareness level affects the rates of infection, vaccination, recovery, and disease progression. The basic reproduction number ($ \mathcal{R}_0 $) is calculated using the next-generation matrix method. The equilibrium points are determined, and their stability analysis is conducted. Disease-free equilibrium (DFE) is globally asymptotically stable for $ \mathcal{R}_0 < 1 $. Forward transcritical bifurcation occurs at $ \mathcal{R}_0 = 1 $. Furthermore, optimal control theory is employed using Pontryagin's maximum principle, with the objective of minimizing infection rates through optimal vaccination at the minimum cost of control. These results are validated by numerical simulations. The results show that effective HPV awareness campaigns can help control the spread of HPV infections, making it easier to manage cervical cancer. This study confirms the importance of awareness-induced behavioral dynamics in modeling spread of HPV for efficient disease management. Awareness campaigns with optimal vaccination can significantly lower HPV transmission and reduce the incidence of cervical cancer.
- basic reproduction number ($ \mathcal{R}_0 $),
- sensitivity analysis,
- equilibria and stability,
- forward bifurcation,
- optimal control approach,
- numerical simulations
Citation: Khalid Aldawsari, Fahad Al Basir. Mathematical modeling and optimal control of HPV-related cervical cancer through awareness campaigns and vaccination[J]. Networks and Heterogeneous Media, 2026, 21(4): 1146-1171. doi: 10.3934/nhm.2026046

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Abstract

In this research, we have derived a mathematical model to study the impact of health center-based awareness campaigns on the spread of human papillomavirus (HPV) infection to cervical cancer. In the model, the human population is divided into susceptible, vaccinated, permanently immune, infected with HPV, and recovered. Moreover, awareness level is assumed as a model compartment. The awareness level affects the rates of infection, vaccination, recovery, and disease progression. The basic reproduction number ($ \mathcal{R}_0 $) is calculated using the next-generation matrix method. The equilibrium points are determined, and their stability analysis is conducted. Disease-free equilibrium (DFE) is globally asymptotically stable for $ \mathcal{R}_0 < 1 $. Forward transcritical bifurcation occurs at $ \mathcal{R}_0 = 1 $. Furthermore, optimal control theory is employed using Pontryagin's maximum principle, with the objective of minimizing infection rates through optimal vaccination at the minimum cost of control. These results are validated by numerical simulations. The results show that effective HPV awareness campaigns can help control the spread of HPV infections, making it easier to manage cervical cancer. This study confirms the importance of awareness-induced behavioral dynamics in modeling spread of HPV for efficient disease management. Awareness campaigns with optimal vaccination can significantly lower HPV transmission and reduce the incidence of cervical cancer.

References

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