The challenge posed by malaria disease calls for an urgent need for a better understanding of important parameters in the disease transmission and development of prevention and control of the spread of malaria disease. In this work, a mathematical model for the dynamics of malaria disease is developed and analyzed. There is existence of disease free equilibrium and endemic equilibrium point of the model, the local stability of disease free equilibrium is obtained using Jacobian matrix which is locally asymptotically stable whenever the basic reproduction number is less than unity. Finally, the results obtained in Table 2, Figure 6 and Figure 8 from sensitivity analysis reveal that malaria disease can be controlled if the biting rate of mosquito is eliminated in the population.

This research is set to investigate non-linear programming problem that is, quadratic programming and its application to portfolio management. The data of return on asset of five different insurance companies namely: AIICO, LINKAGE, NIGER, MUTUAL BENEFIT, and LASACO insurance company was collected and a model was fixed. These data were analyzed using quadratic programming in conjunction with LINDO software. The result of the analyzed data revealed that the allocation of fund for each insurance company should be done with the same percent for LINKAGE, NIGER, MUTUAL BENEFIT and other percent to AIICO insurance company respectively with increment of 24% on return. The research has answered the question of how much an investor should allocate to each investment to minimize risk and maximize return.