Mathematical modelling of liver cancer in Western Kenya

Liver cancer, also known as hepatocellular carcinoma (HCC) is a primary cancer of the liver and the fifth cause of mortality world-wide. It is a global public health problem which is poorly addressed in the developing countries. Data on prevalence and incidence is scanty leading to inability to predict the burden of HCC in the developing world and this leads to poor policy framework for management and control of HCC. More-over, management and control of HCC is poorly addressed in Kenya. Most subjects with HCC in the developing world present late to the hospital leading to high mortality. The objectives of this study were to develop a predictive mathematical model to predict the proportion of subjects who would develop HCC over 5 years in western Kenya and to conduct a sensitivity analysis of the model developed to ascertain effectiveness in prediction. Liver cancer is the only cancer with both infectious and non-infectious causes. The design of the study was a hybrid mathematical model developed integrating both I.P.M (incidence, prevalence, mortality) and S.I.R (susceptible, infected, recovered) models. Ordinary differential equations were generated and solved using Matlab software to predict burden of HCC. MatLab software was also used to generate graphs to predict the number of subjects who will develop HCC over time. Parameters used were generated from empirical data from the study and secondary sources. The study was approved by the ethics committee at Jaramogi Oginga Odinga teaching and referral hospital. The study site was Kisumu county and referral hospital and was conducted between June 2015 and June 2016. Out of 331 (231 males and 100 females) subjects screened, 257 (178 males and 79 females) subjects were included and 74 (50 males and 24 females) were excluded (no liver cancer). Ordinary differential equations were developed which included temporal parameters in the model which were the susceptible population, HCC incidence rates, death rates and birth rates. A schematic hybrid model modified from I.P.M + S.I.R model was developed. S.I.R + I.P.M model was used because HCC cases invariably die but some cases of HCC in early stages survive for some time. In conclusion, this study has established the applicability of the hybrid mathematical model from SIR and IPM for liver cancer burden. Liver cancer burden in western Kenya would increase over time unless risk factors are controlled. The models are sensitive and effective in predicting the burden of liver cancer in the community. This study provides health care workers and stake holders with information to enable generation of policy for management and prevention of HCC.