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A Note on the Application of Martingales in a Problem of Non‐Communicable Epidemics
Author(s) -
Biswas S.,
Noor Hamed Saad
Publication year - 1989
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710310415
Subject(s) - martingale (probability theory) , communicable disease , birth–death process , dysplasia , medicine , cervical cancer , mathematics , cancer , pathology , population , public health , environmental health
The present paper is a Martingale approach to some non‐communicable epidemic problem (e.g. cervical cancer). It is assumed the progress of the disease from pre‐cancerous lesions to several grades of dysplasia and ultimately leading to carcinomia in situ and invasive cancer follows by consecutive hittings; and the regression (or the backward movement) from these states to ultimately non cancerous state; may be analogous to consecutive healings. Each hitting and healing thus considered to be a birth and death respectively in the density dependent linear birth and death process. Given that a patient is in some states of dysplasia the problem lies in finding the proportion of patients coming back to noncancerous state and the expected time for the same. Martingales constructed on a linear birth and death process have been employed to answer the problems.