Difference equation model for malaria transmission and disease

Martin Eichner , 1996
Technical report, German Accademic Exchange Service (DAAD)

Harvard School of Public Health, Boston, U.S.A.

Abstract

This report presents a mathematical model on the transmission of malaria infection and on the incidence of disease and death caused by malaria. It explicitly considers the population dynamics of humans, mosquitoes and animal hosts. It furthermore considers maternal antibodies, the acquisition and loss of immunity (premunity) and the influence of the immune status on the acquisition of the infection, on the probability of disease and on the duration of infectivity. It is examined, how untreated, repellant and toxic bednets influence the feeding behavior of the vector, the transmission of infection and the incidence of disease.

For the parameter values chosen in the model, the incidence of disease and death is highest if the annual inoculation rate is in the magnitude of one inoculation per person per year. Untreated and repellent bednets divert mosquitoes from bednet users to nonusers and thereby change the annual inoculation rates for nonusers and bednet users; toxic bednets reduce the annual inoculation rates for both, users and nonusers. Both types of bednets can cause either more or less malaria cases in any of the groups of individuals. It is often the case that the incidence of disease increases in one of the groups when it decreases in the other group of individuals. The interaction between immunity, infection and disease creates a huge variety of possible results (depending on the prevailing epidemiological situation) which renders an intuitive prediction of the outcome of an intervention campaign practically impossible.