The role of diagnosis at early stages to control cervical cancer: a mathematical prediction
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The role of diagnosis at early stages to control cervical cancer: a mathematical prediction Sudip Chakraborty1,a , Amar Debbouche2,b
, Valery Antonov3,c
1 Department of Mathematics, Jadavpur University, Kolkata 700032, India 2 Department of Mathematics, Guelma University, Guelma 24000, Algeria 3 Department of Mathematics, Peter the Great Saint Petersburg Polytechnic University,
Saint Petersburg 195251, Russia Received: 17 August 2020 / Accepted: 25 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper deals with cervical cancer which is the second most common cancer in females and a major cause of death in the world now a days. Detection of symptoms of cervical cancer basically focused at an advance stage. But it is possible to detect cancer at an early stage through diagnosis and screening. The detection through diagnosis at early stages provides the incentive for the primary prevention and helps to slow down the rapid progression of cervical cancer. Considering diagnosis system a time-dependent variable, here we formulate a new mathematical model on cervical cancer considering susceptible human population, cancer patients and diagnosis. This model gives a framework for understanding how early diagnosis increases the chances for cancer patients to be cancer free by providing proper treatment. To explore the in-depth study of the system, we find the basic reproduction number R0 . We analyze and compare the local stability of the equilibrium points of both the systems in the presence and absence of diagnosis. We investigate analytically as well as numerically the causal effect of diagnosis for reducing the cancer patient at an early stage. Furthermore, we enhance the role of diagnosis by using optimal control strategies to prevent the cervical cancer.
1 Introduction Cervical cancer develops from abnormal cells located in the cervix, the lower part of the uterus that connects with vagina. Most cervical cancers are the results of a previous infection with the Human Papillomavirus (HPV) [1–3]. HPV causes precancerous changes in the susceptible cells of the cervix and may result in the development of the cervical cancer [4]. While cervical cancer is generally a slow-developing disease but if it is not detected and treated early, it can spread to other parts of the body and may become a cause of death. Approximately 90% of the deaths from cervical cancer occur in low- and middle-income countries [5]. The high mortality rate from cervical cancer globally could be reduced through
a e-mail: [email protected] b e-mail: [email protected] (corresponding author) c e-mail: [email protected]
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a comprehensive approach that includes prevention through early diagnosis and treatment programmes. Early diagnosis of cancer generally increases the chances for successful treatments by detecting cancer symptomatic patients as early as possible [5,6]. Particularly in count
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