A Periodically-Forced Mathematical Model for the Seasonal Dynamics of Malaria in Mosquitoes

We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate periodic orbits of field-measurable quantities that measure malaria transmission. We integrate this model with an individual-based stochastic simulation model for malaria in humans to compare the effects of insecticide-treated nets (ITNs) and indoor residual spraying (IRS) in reducing malaria transmission, prevalence, and incidence. We show that ITNs are more effective than IRS in reducing transmission and prevalence though IRS would achieve its maximal effects within 2 years while ITNs would need two mass distribution campaigns over several years to do so. Furthermore, the combination of both interventions is more effective than either intervention alone. However, although these interventions reduce transmission and prevalence, they can lead to increased clinical malaria; and all three malaria indicators return to preintervention levels within 3 years after the interventions are withdraw

A Periodically-Forced Mathematical Model for the Seasonal Dynamics of Malaria in Mosquitoes

We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate periodic orbits of field-measurable quantities that measure malaria transmission. We integrate this model with an individual-based stochastic simulation model for malaria in humans to compare the effects of insecticide-treated nets (ITNs) and indoor residual spraying (IRS) in reducing malaria transmission, prevalence, and incidence. We show that ITNs are more effective than IRS in reducing transmission and prevalence though IRS would achieve its maximal effects within 2 years while ITNs would need two mass distribution campaigns over several years to do so. Furthermore, the combination of both interventions is more effective than either intervention alone. However, although these interventions reduce transmission and prevalence, they can lead to increased clinical malaria; and all three malaria indicators return to preintervention levels within 3 years after the interventions are withdrawn

Incorporating genetic selection into individual‐based models of malaria and other infectious diseases

Introduction Control strategies for human infections are often investigated using individual‐based models (IBMs) to quantify their impact in terms of mortality, morbidity and impact on transmission. Genetic selection can be incorporated into the IBMs to track the spread of mutations whose origin and spread are driven by the intervention and which subsequently undermine the control strategy; typical examples are mutations which encode drug resistance or diagnosis‐ or vaccine‐escape phenotypes. Methods and results We simulated the spread of malaria drug resistance using the IBM OpenMalaria to investigate how the finite sizes of IBMs require strategies to optimally incorporate genetic selection. We make four recommendations. Firstly, calculate and report the selection coefficients, s, of the advantageous allele as the key genetic parameter. Secondly, use these values of “s” to calculate the wait time until a mutation successfully establishes itself in the pathogen population. Thirdly, identify the inherent limits of the IBM to robustly estimate small selection coefficients. Fourthly, optimize computational efficacy: when “s” is small, fewer replicates of larger IBMs may be more efficient than a larger number of replicates of smaller size. Discussion The OpenMalaria IBM of malaria was an exemplar and the same principles apply to IBMs of other diseases

Importance of factors determining the effective lifetime of a mass, long-lasting, insecticidal net distribution: a sensitivity analysis

ABSTRACT: BACKGROUND: Long-lasting insecticidal nets (LLINs) reduce malaria transmission by protecting individuals from infectious bites, and by reducing mosquito survival. In recent years, millions of LLINs have been distributed across sub-Saharan Africa (SSA). Over time, LLINs decay physically and chemically and are destroyed, making repeated interventions necessary to prevent a resurgence of malaria. Because its effects on transmission are important (more so than the effects of individual protection), estimates of the lifetime of mass distribution rounds should be based on the effective length of epidemiological protection. METHODS: Simulation models, parameterised using available field data, were used to analyse how the distribution's effective lifetime depends on the transmission setting and on LLIN characteristics. Factors considered were the pre-intervention transmission level, initial coverage, net attrition, and both physical and chemical decay. An ensemble of 14 stochastic individual-based model variants for malaria in humans was used, combined with a deterministic model for malaria in mosquitoes. RESULTS: The effective lifetime was most sensitive to the pre-intervention transmission level, with a lifetime of almost 10 years at an entomological inoculation rate of two infectious bites per adult per annum (ibpapa), but of little more than 2 years at 256 ibpapa. The LLIN attrition rate and the insecticide decay rate were the next most important parameters. The lifetime was surprisingly insensitive to physical decay parameters, but this could change as physical integrity gains importance with the emergence and spread of pyrethroid resistance. CONCLUSIONS: The strong dependency of the effective lifetime on the pre-intervention transmission level indicated that the required distribution frequency may vary more with the local entomological situation than with LLIN quality or the characteristics of the distribution system. This highlights the need for malaria monitoring both before and during intervention programmes, particularly since there are likely to be strong variations between years and over short distances. The majority of SSA's population falls into exposure categories where the lifetime is relatively long, but because exposure estimates are highly uncertain, it is necessary to consider subsequent interventions before the end of the expected effective lifetime based on an imprecise transmission measur

Simulated Impact of RTS,S/AS01 Vaccination Programs in the Context of Changing Malaria Transmission

INTRODUCTION: The RTS,S/AS01 pre-erythrocytic malaria vaccine is in phase III clinical trials. It is critical to anticipate where and how it should be implemented if trials are successful. Such planning may be complicated by changing levels of malaria transmission. METHODS/RESULTS: Computer simulations were used to examine RTS,S/AS01 impact, using a vaccine profile based on phase II trial results, and assuming that protection decays only slowly. Settings were simulated in which baseline transmission (in the absence of vaccine) was fixed or varied between 2 and 20 infectious mosquito bites per person per annum (ibpa) over ten years. Four delivery strategies were studied: routine infant immunization (EPI), EPI plus infant catch-up, EPI plus school-based campaigns, and EPI plus mass campaigns. Impacts in changing transmission settings were similar to those in fixed settings. Assuming a persistent effect of vaccination, at 2 ibpa, the vaccine averted approximately 5-7 deaths per 1000 doses of vaccine when delivered via mass campaigns, but the benefit was less at higher transmission levels. EPI, catch-up and school-based strategies averted 2-3 deaths per 1000 doses in settings with 2 ibpa. In settings where transmission was decreasing or increasing, EPI, catch-up and school-based strategies averted approximately 3-4 deaths per 1000 doses. DISCUSSION: Where transmission is changing, it appears to be sufficient to consider simulations of pre-erythrocytic vaccine impact at a range of initial transmission levels. At 2 ibpa, mass campaigns averted the most deaths and reduced transmission, but this requires further study. If delivered via EPI, RTS,S/AS01 could avert approximately 6-11 deaths per 1000 vaccinees in all examined settings, similar to estimates for pneumococcal conjugate vaccine in African infants. These results support RTS,S/AS01 implementation via EPI, for example alongside vector control interventions, providing that the phase III trials provide support for our assumptions about efficacy

Ensemble Modeling of the Likely Public Health Impact of a Pre-Erythrocytic Malaria Vaccine

Using an ensemble modeling approach, Thomas Smith and colleagues find that targeted mass vaccination with a pre-erythrocytic malaria vaccine RTS,S in low-transmission settings might have better health effects than vaccination through national EPI programs