Mathematical Analysis of an Age-Structured Modelling for Solid Waste Generation Management System and Treatment in Makindye Division of Kampala

Recently, various regulatory policies towards disposal of solid waste generation have not been successful due to improper management of solid waste generation in the communities. This study aimed at assessing the impact of population growth on solid waste generation in Kampala. A deterministic compartmental model is proposed and developed by classifying the population into three age structure and each group has its own rate of solid waste generation and natural death rate using both qualitative and quantitative approaches. The population is assumed to increase due to birth rate and migration rate. Primary data were obtained using a survey questionnaire to 400 respondents in the Makindye Division. The model proposed is analysed qualitatively using the theory of stability differential equations and SPSS software packages. Numerical simulation is employed using Excel Micro Software in order to validate and support the qualitative results. The study found that, both numerical and analytical solutions affirm that the accumulation of solid waste increases with an increase in the fast population growth in the division. The result shows that increase in the solid waste generation treatment effort leads to a decrease in the accumulation of solid waste generation. The results from the data collected revealed that management and environment is significantly correlated with p-value It is also seen from the results that management and health is significantly correlated with a p-value It is concluded that in order to have an environment free of health hazards, concerted treatment effort is required by all stakeholders involved.