Malaria Modeling in the Era of Eradication

Abstract

Mathematical models provide the essential basis of rational research and development strategies in malaria, informing the choice of which technologies to target, which deployment strategies to consider, and which populations to focus on. The Internet and remote sensing technologies also enable assembly of ever more relevant field data. Together with supercomputing technology, this has made available timely descriptions of the geography of malaria transmission and disease across the world and made it possible for policy and planning to be informed by detailed simulations of the potential impact of intervention programs. These information technology advances do not replace the basic understanding of the dynamics of malaria transmission that should be embedded in the thinking of anyone planning malaria interventions. The appropriate use of modeling may determine whether we are living in an era of hubris or indeed in an age of eradication.

Figure 1.

Sensitivity of R₀ to changes in mosquito density, biting rate, and mosquito survival calculated for the Ross–Macdonald model (based on Koella 1991). Macdonald’s formula for R₀ is $R_0=\frac{m{a}^{2}bc{p}^{\tau }}{-\gamma \log \left(p\right)},$ where the different parameters are m = the number of female mosquitoes per human host, a = the number of bites per mosquito per day, b = the probability of transmitting infection from an infectious mosquito to a human (per bite), c = the probability of transmission of infection from an infectious human to a mosquito (per bite), γ = rate of recovery of humans from infectiousness (equivalently, 1/γ, duration of human infectiousness), p = the daily survival of adult mosquitoes, and τ = the period required for development of sporozoites from infection of the mosquito. Changes in parameter values are represented as the efficacy of shown factors relating to the original setting (e.g., an efficacy of 50% corresponds to a multiplication of m, or 1/γ by 0.5; m or 1/γ enter the equation for the basic reproductive number linearly); therefore, this efficacy corresponds to a 50% decrease in reproductive number. Biting rate, a, enters the reproductive number quadratically, so that an efficacy of 50% in reducing this leads to reduction in R₀ to 0.5² = 0.25 times its original value. Efficacy in adulticiding of 50% corresponds to a 50% reduction in survival per unit time. This enters the formula for R₀ as a power function so decreases in this lead to the largest changes in R₀.