Mathematical modeling, spatial complexity, and critical decisions in tsetse control

Does Counting Different Life Stages Impact Estimates for Extinction Probabilities for Tsetse (Glossina spp)?

As insect populations decline, due to climate change and other environmental disruptions, there has been an increased interest in understanding extinction probabilities. Generally, the life cycle of insects occurs in well-defined stages: when counting insects, questions naturally arise about which life stage to count. Using tsetse flies (vectors of trypanosomiasis) as a case study, we develop a model that works when different life stages are counted. Previous branching process models for tsetse populations only explicitly represent newly emerged adult female tsetse and use that subpopulation to keep track of population growth/decline. Here, we directly model other life stages. We analyse reproduction numbers and extinction probabilities and show that several previous models used for estimating extinction probabilities for tsetse populations are special cases of the current model. We confirm that the reproduction number is the same regardless of which life stage is counted, and show how the extinction probability depends on which life stage we start from. We demonstrate, and provide a biological explanation for, a simple relationship between extinction probabilities for the different life stages, based on the probability of recruitment between stages. These results offer insights into insect population dynamics and provide tools that will help with more detailed models of tsetse populations. Population dynamics studies of insects should be clear about life stages and counting points.

Dispersal in heterogeneous environments drives population dynamics and control of tsetse flies

Spatio-temporally heterogeneous environments may lead to unexpected population dynamics. Knowledge is needed on local properties favouring population resilience at large scale. For pathogen vectors, such as tsetse flies transmitting human and animal African trypanosomosis, this is crucial to target management strategies. We developed a mechanistic spatio-temporal model of the age-structured population dynamics of tsetse flies, parametrized with field and laboratory data. It accounts for density- and temperature-dependence. The studied environment is heterogeneous, fragmented and dispersal is suitability-driven. We confirmed that temperature and adult mortality have a strong impact on tsetse populations. When homogeneously increasing adult mortality, control was less effective and induced faster population recovery in the coldest and temperature-stable locations, creating refuges. To optimally select locations to control, we assessed the potential impact of treating them and their contribution to the whole population. This heterogeneous control induced a similar population decrease, with more dispersed individuals. Control efficacy was no longer related to temperature. Dispersal was responsible for refuges at the interface between controlled and uncontrolled zones, where resurgence after control was very high. The early identification of refuges, which could jeopardize control efforts, is crucial. We recommend baseline data collection to characterize the ecosystem before implementing any measures.

Backward Bifurcation and Optimal Control Analysis of a Trypanosoma brucei rhodesiense Model

In this paper, a mathematical model for the transmission dynamics of Trypanosoma brucei rhodesiense that incorporates three species—namely, human, animal and vector—is formulated and analyzed. Two controls representing awareness campaigns and insecticide use are investigated in order to minimize the number of infected hosts in the population and the cost of implementation. Qualitative analysis of the model showed that it exhibited backward bifurcation generated by awareness campaigns. From the optimal control analysis we observed that optimal awareness and insecticide use could lead to effective control of the disease even when they were implemented at low intensities. In addition, it was noted that insecticide control had a greater impact on minimizing the spread of the disease compared to awareness campaigns.

Negative Density-dependent Dispersal in Tsetse Flies: A Risk for Control Campaigns?

Tsetse flies are vectors of parasites that cause diseases responsible for significant economic losses and health issues in sub-Saharan Africa, including sleeping sickness in humans and nagana in domestic animals. Efficient vector-control campaigns require good knowledge of the demographic parameters of the targeted populations. In the last decade, population genetics emerged as a convenient way to measure population densities and dispersal in tsetse flies. Here, by revealing a strong negative density-dependent dispersal in two dimensions, we suggest that control campaigns might unleash dispersal from untreated areas. If confirmed by direct measurement of dispersal before and after control campaigns, area-wide and/or sequential treatments of neighboring sites will be necessary to prevent this issue.

An agent-based model to simulate tsetse fly distribution and control techniques: a case study in Nguruman, Kenya

BACKGROUND

African trypanosomiasis, also known as "sleeping sickness" in humans and "nagana" in livestock is an important vector-borne disease in Sub-Saharan Africa. Control of trypanosomiasis has focused on eliminating the vector, the tsetse fly (Glossina, spp.). Effective tsetse fly control planning requires models to predict tsetse population and distribution changes over time and space. Traditional planning models have used statistical tools to predict tsetse distributions and have been hindered by limited field survey data.

METHODOLOGY/RESULTS

We developed an Agent-Based Model (ABM) to provide timing and location information for tsetse fly control without presence/absence training data. The model is driven by daily remotely-sensed environment data. The model provides a flexible tool linking environmental changes with individual biology to analyze tsetse control methods such as aerial insecticide spraying, wild animal control, releasing irradiated sterile tsetse males, and land use and cover modification.

SIGNIFICANCE

This is a bottom-up process-based model with freely available data as inputs that can be easily transferred to a new area. The tsetse population simulation more closely approximates real conditions than those using traditional statistical models making it a useful tool in tsetse fly control planning.

Mathematical models of human african trypanosomiasis epidemiology

Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.