Ticks and tick-borne diseases: a vector-host interaction model for the brown ear tick (Rhipicephalus appendiculatus)

Modeling Lyme disease transmission

Lyme disease, a typical tick-borne disease, imposes increasing global public health challenges. A growing body of theoretical models have been proposed to better understand various factors determining the disease risk, which not only enrich our understanding on the ecological cycle of disease transmission but also promote new theoretical developments on model formulation, analysis and simulation. In this paper, we provide a review about the models and results we have obtained recently on modeling and analyzing Lyme disease transmission, with the purpose to highlight various aspects in the ecological cycle of disease transmission to be incorporated, including the growth of ticks with different stages in the life cycle, the seasonality, host diversity, spatial disease pattern due to host short distance movement and bird migration, co-infection with other tick-borne pathogens, and climate change impact.

The Role of Hyalomma Truncatum on the Dynamics of Rift Valley Fever: Insights from a Mathematical Epidemic Model

To date, our knowledge of Rift Valley fever (RVF) disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive an explicit formula of the basic reproductive number, [Formula: see text]. Using the concept of Metzler matrix, we state necessary conditions for global asymptotic stability of the disease-free equilibrium. Results suggest that although host-ticks interactions may serve as disease reservoirs or disease amplifiers, the Aedes reproductive number should be kept under unity if disease post-epizootics activities are to be controlled. Results of both local and global sensitivity analysis of selected model parameters indicate that [Formula: see text] is more sensitive to the ticks attachment and detachment rates, probability of transmission from ticks to host and from host to ticks, length of infection in livestock and ticks death rate. Furthermore, when comparing the mean value of [Formula: see text] with that from previous studies which did not include ticks we found that our [Formula: see text] is very much larger resulting in an increase in the exponential phase of an outbreak. These findings suggest that if ticks are capable of transmitting the virus, they may be contributing to disease outbreaks and endemicity.

Impact of biodiversity and seasonality on Lyme-pathogen transmission

Lyme disease imposes increasing global public health challenges. To better understand the joint effects of seasonal temperature variation and host community composition on the pathogen transmission, a stage-structured periodic model is proposed by integrating seasonal tick development and activity, multiple host species and complex pathogen transmission routes between ticks and reservoirs. Two thresholds, one for tick population dynamics and the other for Lyme-pathogen transmission dynamics, are identified and shown to fully classify the long-term outcomes of the tick invasion and disease persistence. Seeding with the realistic parameters, the tick reproduction threshold and Lyme disease spread threshold are estimated to illustrate the joint effects of the climate change and host community diversity on the pattern of Lyme disease risk. It is shown that climate warming can amplify the disease risk and slightly change the seasonality of disease risk. Both the "dilution effect" and "amplification effect" are observed by feeding the model with different possible alternative hosts. Therefore, the relationship between the host community biodiversity and disease risk varies, calling for more accurate measurements on the local environment, both biotic and abiotic such as the temperature and the host community composition.

Delay differential systems for tick population dynamics

Ticks play a critical role as vectors in the transmission and spread of Lyme disease, an emerging infectious disease which can cause severe illness in humans or animals. To understand the transmission dynamics of Lyme disease and other tick-borne diseases, it is necessary to investigate the population dynamics of ticks. Here, we formulate a system of delay differential equations which models the stage structure of the tick population. Temperature can alter the length of time delays in each developmental stage, and so the time delays can vary geographically (and seasonally which we do not consider). We define the basic reproduction number [Formula: see text] of stage structured tick populations. The tick population is uniformly persistent if [Formula: see text] and dies out if [Formula: see text]. We present sufficient conditions under which the unique positive equilibrium point is globally asymptotically stable. In general, the positive equilibrium can be unstable and the system show oscillatory behavior. These oscillations are primarily due to negative feedback within the tick system, but can be enhanced by the time delays of the different developmental stages.

Persistent oscillations and backward bifurcation in a malaria model with varying human and mosquito populations: implications for control

We derive and study a deterministic compartmental model for malaria transmission with varying human and mosquito populations. Our model considers disease-related deaths, asymptomatic immune humans who are also infectious, as well as mosquito demography, reproduction and feeding habits. Analysis of the model reveals the existence of a backward bifurcation and persistent limit cycles whose period and size is determined by two threshold parameters: the vectorial basic reproduction number Rm, and the disease basic reproduction number R0, whose size can be reduced by reducing Rm. We conclude that malaria dynamics are indeed oscillatory when the methodology of explicitly incorporating the mosquito's demography, feeding and reproductive patterns is considered in modeling the mosquito population dynamics. A sensitivity analysis reveals important control parameters that can affect the magnitudes of Rm and R0, threshold quantities to be taken into consideration when designing control strategies. Both Rm and the intrinsic period of oscillation are shown to be highly sensitive to the mosquito's birth constant λm and the mosquito's feeding success probability pw. Control of λm can be achieved by spraying, eliminating breeding sites or moving them away from human habitats, while pw can be controlled via the use of mosquito repellant and insecticide-treated bed-nets. The disease threshold parameter R0 is shown to be highly sensitive to pw, and the intrinsic period of oscillation is also sensitive to the rate at which reproducing mosquitoes return to breeding sites. A global sensitivity and uncertainty analysis reveals that the ability of the mosquito to reproduce and uncertainties in the estimations of the rates at which exposed humans become infectious and infectious humans recover from malaria are critical in generating uncertainties in the disease classes.