Stability of Cervical Cancer Model by Human Papillomavirrus (HPV) with Migration

Irma Suryani; Mohammad Soleh; Wartono Wartono; Anggi Prayoga; Boby Fahlezi

doi:10.30829/zero.v8i1.16137

Stability of Cervical Cancer Model by Human Papillomavirrus (HPV) with Migration

Irma Suryani, Mohammad Soleh, Wartono Wartono, Anggi Prayoga, Boby Fahlezi

Abstract

Cervical cancer is a chronic disease that attacks the cervix. This disease is caused by the human papillomavirus (HPV). Over time, cervical cancer is modeled with a mathematical model to describe the development of its spread. In this study, cervical cancer is modeled into four subpopulations; susceptible subpopulation (S), HPV-infected subpopulation (I), infected but not infected with cervical cancer (U) and infected and infected with cervical cancer (C). The SIUC model is then added to the existence of migration within the population. Furthermore, the equilibrium of the model is determine and its stability is analyzed using the Jacobian matrix and eigenvalues. The result is that there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The disease-free equilibrium point is asymptotically stable if the eigenvalue conditions are met. The endemic equilibrium point is stable if the eigenvalues are met. Furthermore, the numerical simulation model shows that migration that occurs within the population can cause cervical cancer to still exist in the population because the contact rate is getting bigger

Keywords

Eigen Values, Equilibrium, Jacobian Matrix, Model of Cervical Cancer SIUC

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DOI: http://dx.doi.org/10.30829/zero.v8i1.16137

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Department of Mathematics
Faculty of Science and Technology
Universitas Islam Negeri Sumatera Utara Medan

Email: mtk.saintek@uinsu.ac.id

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