Modeling the Effects of Malaria Preventative Measures

Abstract

Malaria is a serious and sometimes fatal epidemic affecting nearly half of the world's population and is the 5th leading cause of death by infectious disease world-wide. There are currently two recommended methods for prevention and eradication of the disease: insecticide-treated mosquito nets (ITNs) and indoor residual spraying (IRS), but efficacies and compliance vary from region to region. In this project, we look at the effects of ITNs and IRS as methods for eradication of malaria. To compare these methods, we develop a differential equation model and apply the next generation matrix method to determine the basic reproductive number. The differential equation model builds on classical SIR epidemiological models, with added constraints for the two preventative measures. Analysis shows that the effects of ITNs and IRS can help eradicate the disease. We find that the effect of ITNs is significantly greater than the effect of IRS. We conclude that the combination of compliance and efficacy for ITNs needs to be at least 61% and that there is no such percentage for IRS alone that will eradicate the disease. At a minimum, in combination, compliance and efficacy for ITNs needs to be at least 60% and compliance and efficacy for IRS needs to be at least 60%.

A comprehensive model of spread of malaria in humans and mosquitos

“…The compartments are: Susceptible -Exposed -Infected (SEI). Since, the mosquitos can't be treated of malaria, so we assume that all the infected mosquitos eventually die and this assumption is coherent with other studies [17]. Figure 2 shows the model.…”

Solutions of a disease model with fractional white noise

“…These systems were generated by taking into account some facts such as duration of disease, availability and resistance against vaccination, immune systems of individuals in the population and so on. There are mathematical models employing deterministic [4][5][6][7] , stochastic [1][2][3] , fractional-order [8][9][10][11][12][13][14][15] system of differential equations. Almost each of these models were generated by compartmental models considering each compartment as individuals of susceptible (denoted by S), infected (I), exposed (E), and recovered (R) ones.…”