Orthogonality of elementary operators in normed spaces and their applications

Abstract

Malaria is a major public health concern, especially among pregnant women and children under the age of five. It is a leading cause of morbidity and mortality in Malawi, accounting for fourty percent of out-patient consultations in many health facilities in the country. Mathematical models have an important role to play in making public health decisions about the control of infectious diseases such that they are better informed and more objective. In order to understand the prevalence, transmission and control of the Malaria epidemic, an SEIR model has been used in this study. The model was analysed to determine criteria for control of the malaria epidemic, and was used to compute the basic reproduction and effective reproduction numbers necessary for control of the disease. In this paper an expression for the basic reproduction number R0 is derived through the next generation method. Numerical results indicate the effect of the two controls: protection and treatment in lowering exposed and infected members of each of the populations. The results also highlight the effects of infection rate and removal rate.