Spatial dynamics of malaria transmission.

The Ross-Macdonald model has exerted enormous influence over the study of malaria transmission dynamics and control, but it lacked features to describe parasite dispersal, travel, and other important aspects of heterogeneous transmission. Here, we present a patch-based differential equation modeling framework that extends the Ross-Macdonald model with sufficient skill and complexity to support planning, monitoring and evaluation for Plasmodium falciparum malaria control. We designed a generic interface for building structured, spatial models of malaria transmission based on a new algorithm for mosquito blood feeding. We developed new algorithms to simulate adult mosquito demography, dispersal, and egg laying in response to resource availability. The core dynamical components describing mosquito ecology and malaria transmission were decomposed, redesigned and reassembled into a modular framework. Structural elements in the framework-human population strata, patches, and aquatic habitats-interact through a flexible design that facilitates construction of ensembles of models with scalable complexity to support robust analytics for malaria policy and adaptive malaria control. We propose updated definitions for the human biting rate and entomological inoculation rates. We present new formulas to describe parasite dispersal and spatial dynamics under steady state conditions, including the human biting rates, parasite dispersal, the "vectorial capacity matrix," a human transmitting capacity distribution matrix, and threshold conditions. An [Formula: see text] package that implements the framework, solves the differential equations, and computes spatial metrics for models developed in this framework has been developed. Development of the model and metrics have focused on malaria, but since the framework is modular, the same ideas and software can be applied to other mosquito-borne pathogen systems.

Infection age as a predictor of epidemiological metrics for malaria.

BACKGROUND: Accurate estimation of the burden of Plasmodium falciparum is essential for strategic planning for control and elimination. Due in part to the extreme heterogeneity in malaria exposure, immunity, other causes of disease, direct measurements of fever and disease attributable to malaria can be difficult. This can make a comparison of epidemiological metrics both within and between populations hard to interpret. An essential part of untangling this is an understanding of the complex time-course of malaria infections. METHODS: Historic data from malariatherapy infections, in which individuals were intentionally infected with malaria parasites, were reexamined in aggregate. In this analysis, the age of each infection was examined as a potential predictor describing aggregate patterns across all infections. A series of piecewise linear and generalized linear regressions were performed to highlight the infection age-dependent patterns in both parasitaemia and gametocytaemia, and from parasitaemia and gametocytaemia to fever and transmission probabilities, respectively. RESULTS: The observed duration of untreated patent infection was 130 days. As infections progressed, the fraction of infections subpatent by microscopy was seen to increase steadily. The time-averaged malaria infections had three distinct phases in parasitaemia: a growth phase for the first 6 days of patency, a rapid decline from day 6 to day 18, and a slowly declining chronic phase for the remaining duration of the infection. During the growth phase, parasite densities increased sharply to a peak. Densities sharply decline for a short period of time after the peak. During the chronic phase, infections declined steadily as infections age. gametocytaemia was strongly correlated with lagged asexual parasitaemia. Fever rates and transmission efficiency were strongly correlated with parasitaemia and gametocytaemia. The comparison between raw data and prediction from the age of infection has good qualitative agreement across all quantities of interest for predicting averaged effects. CONCLUSION: The age of infection was established as a potentially useful covariate for malaria epidemiology. Infection age can be estimated given a history of exposure, and accounting for exposure history may potentially provide a new way to estimate malaria-attributable fever rates, transmission efficiency, and patent fraction in immunologically naïve individuals such as children and people in low-transmission regions. These data were collected from American adults with neurosyphilis, so there are reasons to be cautious about extending the quantitative results reported here to general populations in malaria-endemic regions. Understanding how immune responses modify these statistical relationships given past exposure is key for being able to apply these results more broadly.

Comparing metapopulation dynamics of infectious diseases under different models of human movement.

Newly available datasets present exciting opportunities to investigate how human population movement contributes to the spread of infectious diseases across large geographical distances. It is now possible to construct realistic models of infectious disease dynamics for the purposes of understanding global-scale epidemics. Nevertheless, a remaining unanswered question is how best to leverage the new data to parameterize models of movement, and whether one's choice of movement model impacts modeled disease outcomes. We adapt three well-studied models of infectious disease dynamics, the susceptible-infected-recovered model, the susceptible-infected-susceptible model, and the Ross-Macdonald model, to incorporate either of two candidate movement models. We describe the effect that the choice of movement model has on each disease model's results, finding that in all cases, there are parameter regimes where choosing one movement model instead of another has a profound impact on epidemiological outcomes. We further demonstrate the importance of choosing an appropriate movement model using the applied case of malaria transmission and importation on Bioko Island, Equatorial Guinea, finding that one model produces intelligible predictions of R0, whereas the other produces nonsensical results.

Vector bionomics and vectorial capacity as emergent properties of mosquito behaviors and ecology.

Mosquitoes are important vectors for pathogens that infect humans and other vertebrate animals. Some aspects of adult mosquito behavior and mosquito ecology play an important role in determining the capacity of vector populations to transmit pathogens. Here, we re-examine factors affecting the transmission of pathogens by mosquitoes using a new approach. Unlike most previous models, this framework considers the behavioral states and state transitions of adult mosquitoes through a sequence of activity bouts. We developed a new framework for individual-based simulation models called MBITES (Mosquito Bout-based and Individual-based Transmission Ecology Simulator). In MBITES, it is possible to build models that simulate the behavior and ecology of adult mosquitoes in exquisite detail on complex resource landscapes generated by spatial point processes. We also developed an ordinary differential equation model which is the Kolmogorov forward equations for models developed in MBITES under a specific set of simplifying assumptions. While mosquito infection and pathogen development are one possible part of a mosquito's state, that is not our main focus. Using extensive simulation using some models developed in MBITES, we show that vectorial capacity can be understood as an emergent property of simple behavioral algorithms interacting with complex resource landscapes, and that relative density or sparsity of resources and the need to search can have profound consequences for mosquito populations' capacity to transmit pathogens.

A hybrid model for the effects of treatment and demography on malaria superinfection.

As standard mathematical models for the transmission of vector-borne pathogens with weak or no apparent sterilizing immunity, Susceptible-Infected-Susceptible (SIS) systems such as the Ross-Macdonald equations are a useful starting point for modeling the impacts of interventions on prevalence for diseases that cannot superinfect their hosts. In particular, they are parameterizable from quantities we can estimate such as the force of infection (FOI), the rate of natural recovery from a single infection, the treatment rate, and the rate of demographic turnover. However, malaria parasites can superinfect their host which has the effect of increasing the duration of infection before total recovery. Queueing theory has been applied to capture this behavior, but a problem with current queueing models is the exclusion of factors such as demographic turnover and treatment. These factors in particular can affect the entire shape of the distribution of the multiplicity of infection (MOI) generated by the superinfection process, its transient dynamics, and the population mean recovery rate. Here we show the distribution of MOI can be described by an alternative hyper-Poisson distribution. We then couple our resulting equations to a simple vector transmission model, extending previous Ross-Macdonald theory.