Browsing by Author "Pokhariyal, G. P."
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Item Analytical model for childhood pneumonia, a case study of Kenya(Science Domain International, 2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.Pneumonia is an infection of the lungs that is caused by bacteria, viruses, fungi, or parasites. For a long time to the best of our knowledge there have not been reliable mathematical model for childhood pneumonia in Kenya. This research study developed a deterministic model based on the Susceptible- Vaccinated-Infected-Treated-Recovered-Susceptible compartment classes. The study used the partial differentiation of control reproduction number toinvestigate effects of; environment, efficacy of vaccination drug and treatment. Model analysis indicates the system lie in feasible region, it is bounded, has no backward bifurcation and there exists unique endemic equilibrium point when control reproduction number is greater than unity. Local and global stability of the equilibrium points indicated that control reproduction has to be maintained at less than unity to eradicate the disease. Sensitivity analysis of the control reproduction number indicates that improved vaccination drug’s efficacy, attaining herd immunity, higher treatment rates and lower effects of environment are the best intervention strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.Item Estimated numerical results for the deterministic model of the under five years pneumonia in Kenya(2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.In this paper the numerical results are estimated for childhood pneumonia deterministic model, using Kenyan data. The estimates of data and parameters from Kenya Health information system, ministry of Health of Kenya and UNICEF for the years 2012 and 2013 were fitted in the developed model using Matlab software. The estimated numerical value for control reproduction number (Rc) and basic reproduction number (Ro) were obtained as 9.31808 and 22.5914 respectively, by substituting estimated parameters in the expression for the determined analytical results. The herd immunity was estimated as 95.57% using the basic reproduction number. Impact of treatment value was found to be found to be positive. Sensitivity analysis of the control reproduction number indicates that improved vaccination drug’s efficacy, attaining herd immunity, higher treatment rates and lower effects of environment are the best intervention strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.Item Numerical simulation of the deterministic model of the under-five year’s pneumonia in Kenya(2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.In this paper the numerical simulation of the childhood pneumonia deterministic model are determined. The estimated parameters and the under-five year’s population data for year 2013 was used to simulate the developed deterministic model, using Matlab inbuilt ordinary differential equation (ode) solver. Graphical results predicting the dynamics of the under-five year’s pneumonia were obtained for a period of twenty years. Simulations indicated that sustained vaccination and treatment are likely to reduce the burden of the under-five year’s pneumonia over a period twenty years.