Factors affecting onchocerciasis transmission: Lessons for infection control

Introduction: Onchocerca volvulus infects in excess of 15 million people. The vectors are Simulium blackflies, varieties of which differ in their ecologies, behaviour and vectorial abilities. Control of the vectors and mass administrations of ivermectin have succeeded in reducing prevalences with elimination achieved in some foci, particularly in Central and southern America. In Africa, progress towards elimination has been less successful. Areas covered: Even with community directed treatment with ivermectin (CDTI), control has been difficult in African areas with initial prevalences in excess of 55%, especially if only annual treatments are dispensed. This is partly attributable to insufficient coverage, but the appearance of incipiently resistant non-responding parasites and lack of attention to vector biology in modelling and planning outcomes of intervention programmes have also played their parts, with recrudescence now appearing in some treated areas. Expert commentary: The biology of onchocerciasis is complex involving different vectors with differing abilities to transmit parasites, diverse pathologies related to geographical and parasite variations and endosymbionts in both parasite and vector. Modelling to predict epidemiological and control outcomes is addressing this complexity but more attention needs to be given to the vectors’ roles to further understanding of where and when control measures will succeed

Desert locust populations, rainfall and climate change: insights from phenomenological models using gridded monthly data

Using autocorrelation analysis and autoregressive integrated moving average (ARIMA)modelling, we analysed a time series of the monthly number of 1° grid squares infested with desert locust Schistocerca gregaria swarms throughout the geographical range of the species from 1930–1987. Statistically significant first- and higher-order autocorrelations were found in the series. Although endogenous components captured much of the variance, adding rainfall data improved endogenous ARIMA models and resulted in more realistic forecasts. Using a square-root transformation for the locust data improved the fit. The models were only partially successful when accounting for the dramatic changes in abundance which may occur during locust upsurges and declines, in some cases successfully predicting these phenomena but underestimating their severity. Better fitting models were also produced when rainfall data were added to models of an equivalent series for desert locust hoppers (nymphs) that incorporated lagged data for locust swarms as independent variables, representing parent generations. The results are discussed in relation to predicting likely changes in desert locust dynamics with reference to potential effects of climate change

Ecological characteristics of Simulium breeding sites in West Africa

Twenty-nine taxa of Simulium were identified amongst 527 collections of larvae and pupae from untreated rivers and streams in Liberia (362 collections in 1967–71 & 1989), Togo (125 in 1979–81), Benin (35 in1979–81) and Ghana (5 in 1980–81). Presence or absence of associations between different taxa were usedto group them into six clusters using Ward agglomerative hierarchical cluster analysis. Environmental data associated with the pre-imaginal habitats were then analysed in relation to the six clusters by oneway ANOVA. The results revealed significant effects in determining the clusters of maximum river width (all P < 0.001 unless stated otherwise), water temperature, dry bulb air temperature, relative humidity,altitude, type of water (on a range from trickle to large river), water level, slope, current, vegetation,light conditions, discharge, length of breeding area, environs, terrain, river bed type (P < 0.01), and the supports to which the insects were attached (P < 0.01). When four non-significant contributors (wet bulb temperature, river features, height of waterfall and depth) were excluded and the reduced data-set analysed by principal components analysis (PCA), the first two principal components (PCs) accounted for 87% of the variance, with geographical features dominant in PC1 and hydrological characteristics in PC2. The analyses also revealed the ecological characteristics of each taxon’s pre-imaginal habitats, which are discussed with particular reference to members of the Simulium damnosum species complex, whose breeding site distributions were further analysed by canonical correspondence analysis (CCA), a method also applied to the data on non-vector species

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic

A threshold policy to interrupt transmission of West Nile Virus to birds

This paper proposes a model of West Nile Virus (WNV) with a Filippov-type control strategy of culling mosquitoes implemented once the number of infected birds exceeds a threshold level. The long-term dynamical behaviour of the proposed non-smooth system is investigated. It is shown hat as the threshold value varies, model solutions ultimately approach either one of two endemic equilibria for two subsystems or a pseudo-equilibrium on the switching surface, which is a novel steady state. The results indicate that a previously chosen level of infected birds can be maintained when the threshold policy and other parameters are chosen properly. Numerical studies show that under the threshold policy, strengthening mosquito culling together with protecting bird population is beneficial to curbing the spread of WNV

Models of impulsive culling of mosquitoes to interrupt transmission of West Nile Virus to birds

A mathematical model describing the transmission of West Nile virus (WNV) between vector mosquitoes and birds, incorporating a control strategy of culling mosquitoes and defined by impulsive differential equations is presented and its properties investigated. First, we consider a strategy of periodic impulsive culling of the mosquitoes. Theoretical results indicate that if the threshold R 0 is greater than unity the disease uniformly persists, but, if not, the disease does not necessarily become extinct. The explicit conditions determining the backward or forward bifurcation were obtained. The culling rate has a major effect on the occurrence of backward bifurcation. Analysis shows that the disease is most sensitive to mosquito-bird contacts, mosquito-culling rate and intervals between culls. The dependence of the outcomes of the culling strategy on mosquito biting rate is discussed. When the complete elimination of disease is impossible, mosquito culls are implemented once the infected birds reach a predefined but adjustable threshold value. Numerical analysis shows that the period of mosquito culling finally stabilizes at a fixed value. In addition, variations of mean prevalence of \{WNV\} in birds and the culling period are simulated

Global dynamics of a piece-wise epidemic model with switching vaccination strategy

A piece-wise epidemic model of a switching vaccination program, implemented once the number of people exposed to a disease-causing virus reaches a critical level, is proposed. In addition, variation or uncertainties in interventions are examined with a perturbed system version of the model. We also analyzed the global dynamic behaviors of both the original piece-wise system and the perturbed version theoretically, using generalized Jacobian theory, Lyapunov constants for a non-smooth vector field and a generalization of Dulac's criterion. The main results show that, as the critical value varies, there are three possibilities for stabilization of the piece-wise system: (i) at the disease-free equilibrium; (ii) at the endemic states for the two subsystems or (iii) at a generalized equilibrium which is a novel global attractor for non-smooth systems. The perturbed system exhibits new global attractors including a pseudo-focus of parabolic-parabolic (PP) type, a pseudo-equilibrium and a crossing cycle surrounding a sliding mode region. Our findings demonstrate that an infectious disease can be eradicated either by increasing the vaccination rate or by stabilizing the number of infected individuals at a previously given level, conditional upon a suitable critical level and the parameter values

The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses

The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Furthermore,when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results

Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Periodical applications of immunotherapy and chemotherapy play significant roles in cancer treatment and studies have shown that the evolution of tumour cells is subject to random events. In order to capture the effects of such noise we developed a stochastic tumour-immune dynamical model with pulsed treatment to describe combinations of immunotherapy with chemotherapy. By using theorems of the impulsive stochastic dynamical equation, the tumour free solution and the global positive solution of the proposed system were investigated. We then show that the expectations of the solutions are bounded. Furthermore, threshold conditions for extinction, non-persistence in the mean, weak persistence and stochastic persistence of tumour cells are provided. The results reveal that comprehensive therapy or noise can dominate the evolution of tumours. Finally, biological implications are addressed and a conclusion is presented

Nonlinear pulse vaccination in an SIR epidemic model with resource limitation

Mathematical models can assist in the design and understanding of vaccination strategies when resources are limited. Here we propose and analyse an SIR epidemic modelwith a nonlinear pulse vaccination to examine how a limited vaccine resource affects the transmission and control of infectious diseases, in particular emerging infectious diseases. The threshold condition for the stability of the disease free steady state is given. Latin Hypercube Sampling/Partial Rank Correlation Coefficient uncertainty and sensitivity analysis techniques were employed to determine the key factors which are most significantly related to the threshold value. Comparing this threshold value with that without resource limitation, our results indicate that if resources become limited pulse vaccination should be carried out more frequently than when sufficient resources are available to eradicate an infectious disease. Once the threshold value exceeds a critical level, both susceptible and infected populations can oscillate periodically. Furthermore, when the pulse vaccination period is chosen as a bifurcation parameter, the SIR model with nonlinear pulse vaccination reveals complex dynamics including period doubling, chaotic solutions, and coexistence of multiple attractors. The implications of our findings with respect to disease control are discussed