A generalized risk assessment index for forecasting insect population under the effect of temperature.

Life history traits have been studied under various environmental factors, but the ability to combine them into a simple function to assess pest response to climate is still lacking complete understanding. This study proposed a risk index derived by combining development, mortality, and fertility rates from a stage-structured dynamic mathematical model. The first part presents the theoretical framework behind the risk index. The second part of the study is concerned with the application of the index in two case studies of major economic pest: the brown planthopper (Nilaparvata lugens) and the spotted wing drosophila (Drosophila suzukii), pests of rice crops and soft fruits, respectively. The mathematical calculations provided a single function composed of the main thermal biodemographic rates. This function has a threshold value that determines the possibility of population increase as a function of temperature. The tests carried out on the two pest species showed the capability of the index to describe the range of favourable conditions. With this approach, we were able to identify areas where pests are tolerant to climatic conditions and to project them on a geospatial risk map. The theoretical background developed here provided a tool for understanding the biogeography of Nilaparvata lugens and Drosophila suzukii. It is flexible enough to deal with mathematically simple (N. lugens) and complex (D. Suzukii) case studies of crop insect pests. It produces biologically sound indices that behave like thermal performance curves. These theoretical results also provide a reasonable basis for addressing the challenge of pest management in the context of seasonal weather variations and climate change. This may help to improve monitoring and design management strategies to limit the spread of pests in invaded areas, as some non-invaded areas may be suitable for the species to develop.

Amplitude response, Melnikov's criteria, and chaos occurrence in a Duffing's system subjected to an external periodic excitation with a variable shape.

The present study considers the nonlinear dynamics of a Duffing oscillator under a symmetric potential subjected to a pulse-type excitation with a deformable shape. Our attention is focused on the effects of the external excitation shape parameter r and its period. The frequency response of the system is derived by using a semi-analytical approach. Interestingly, the frequency-response curve displays a large number of resonance peaks and anti-resonance peaks as well. Surprisingly, a resonance phenomenon termed here as shape-induced-resonance is noticed as it occurs solely due to the change in the shape parameter of the external periodic force. The system exhibits amplitude jumps and hysteresis depending on r. The critical driving magnitude for the chaos occurrence is investigated through Melnikov's method. Numerical analysis based on bifurcation diagrams and Lyapunov exponent is used to show how chaos occurs in the system. It is shown that the threshold amplitude of the excitation to observe chaotic dynamics decreases/increases for small/large values of r. In general, the theoretical estimates match with numerical simulations and electronic simulations as well.

Understanding biological control with entomopathogenic fungi-Insights from a stochastic pest-pathogen model.

In this study, an individual-based model is proposed to investigate the effect of demographic stochasticity on biological control using entomopathogenic fungi. The model is formulated as a continuous time Markov process, which is then decomposed into a deterministic dynamics using stochastic corrections and system size expansion. The stability and bifurcation analysis shows that the system dynamic is strongly affected by the contagion rate and the basic reproduction number. However, sensitivity analysis of the extinction probability shows that the persistence of a biological control agent depends to the proportion of spores collected from insect cadavers as well as their ability to be reactivated and infect insects. When considering the migration of each species within a set of patches, the dispersion relation shows a Hopf-damped Turing mode for a threshold contagion rate. A large size population led to a spatial and temporal resonant stochasticity and also induces an amplification effect on power spectrum density.

Theoretical analysis of spatial nonhomogeneous patterns of entomopathogenic fungi growth on insect pest.

This paper presents the study of the dynamics of intrahost (insect pests)-pathogen [entomopathogenic fungi (EPF)] interactions. The interaction between the resources from the insect pest and the mycelia of EPF is represented by the Holling and Powell type II functional responses. Because the EPF's growth is related to the instability of the steady state solution of our system, particular attention is given to the stability analysis of this steady state. Initially, the stability of the steady state is investigated without taking into account diffusion and by considering the behavior of the system around its equilibrium states. In addition, considering small perturbation of the stable singular point due to nonlinear diffusion, the conditions for Turing instability occurrence are deduced. It is observed that the absence of the regeneration feature of insect resources prevents the occurrence of such phenomena. The long time evolution of our system enables us to observe both spot and stripe patterns. Moreover, when the diffusion of mycelia is slightly modulated by a weak periodic perturbation, the Floquet theory and numerical simulations allow us to derive the conditions in which diffusion driven instabilities can occur. The relevance of the obtained results is further discussed in the perspective of biological insect pest control.

Spatial panorama of malaria prevalence in Africa under climate change and interventions scenarios.

BACKGROUND: Malaria is highly sensitive to climatic variables and is strongly influenced by the presence of vectors in a region that further contribute to parasite development and sustained disease transmission. Mathematical analysis of malaria transmission through the use and application of the value of the basic reproduction number (R0) threshold is an important and useful tool for the understanding of disease patterns. METHODS: Temperature dependence aspect of R0 obtained from dynamical mathematical network model was used to derive the spatial distribution maps for malaria transmission under different climatic and intervention scenarios. Model validation was conducted using MARA map and the Annual Plasmodium falciparum Entomological Inoculation Rates for Africa. RESULTS: The inclusion of the coupling between patches in dynamical model seems to have no effects on the estimate of the optimal temperature (about 25 °C) for malaria transmission. In patches environment, we were able to establish a threshold value (about α = 5) representing the ratio between the migration rates from one patch to another that has no effect on the magnitude of R0. Such findings allow us to limit the production of the spatial distribution map of R0 to a single patch model. Future projections using temperature changes indicated a shift in malaria transmission areas towards the southern and northern areas of Africa and the application of the interventions scenario yielded a considerable reduction in transmission within malaria endemic areas of the continent. CONCLUSIONS: The approach employed here is a sole study that defined the limits of contemporary malaria transmission, using R0 derived from a dynamical mathematical model. It has offered a unique prospect for measuring the impacts of interventions through simple manipulation of model parameters. Projections at scale provide options to visualize and query the results, when linked to the human population could potentially deliver adequate highlight on the number of individuals at risk of malaria infection across Africa. The findings provide a reasonable basis for understanding the fundamental effects of malaria control and could contribute towards disease elimination, which is considered as a challenge especially in the context of climate change.

Waves transmission and amplification in an electrical model of microtubules.

Inspired by standard electrophysiological models of microtubules, a discrete nonlinear equation for ionic wave propagation that incorporates a negative nonlinear resistance is presented. The conditions for wave propagation in forbidden band gap are analyzed without and with dissipation. The nonlinear response manifold method is used to determine the supratransmission threshold of the case of study without dissipation. This threshold is found to be similar to the value obtained by analytical methods. With the dissipation, the monitoring of the accumulated energy is used to estimate the infratransmission threshold. It appears that the value of the supratransmission threshold can be lower than the value of the infratransmission threshold. The system is found to amplify significantly the amplitude of the input signal, thus confirming known experimental results. Nevertheless, a proper choice of the parameter of the nonlinear resistance is required for further validation of our results. A possible biological implication of the obtained results is presented.

The effect of climate variability in the efficacy of the entomopathogenic fungus Metarhizium acridum against the desert locust Schistocerca gregaria.

Despite substantial efforts to control locusts they remain periodically a major burden in Africa, causing severe yield loss and hence loss of food and income. Distribution maps indicating the value of the basic reproduction number R0 was used to identify areas where an insect pest can be controlled by a natural enemy. A dynamic process-based mathematical model integrating essential features of a natural enemy and its interaction with the pest is used to generate R0 risk maps for insect pest outbreaks, using desert locust and the entomopathogenic fungus Metarhizium acridum (Synn. Metarhizium anisoliae var. acridum) as a case study. This approach provides a tool for evaluating the impact of climatic variables such as temperature and relative humidity and mapping spatial variability on the efficacy of M. acridum as a biocontrol agent against desert locust invasion in Africa. Applications of M. acridum against desert locust in a few selected African countries including Morocco, Kenya, Mali, and Mauritania through monthly spatial projection of R0 maps for the prevailing climatic condition are illustrated. By combining mathematical modeling with a geographic information system in a spatiotemporal projection as we do in this study, the field implementation of microbial control against locust in an integrated pest management system may be improved. Finally, the practical utility of this model provides insights that may improve the timing of pesticide application in a selected area where efficacy is highly expected.

Stability, bifurcation and chaos analysis of vector-borne disease model with application to Rift Valley fever.

This paper investigates a RVF epidemic model by qualitative analysis and numerical simulations. Qualitative analysis have been used to explore the stability dynamics of the equilibrium points while visualization techniques such as bifurcation diagrams, Poincaré maps, maxima return maps and largest Lyapunov exponents are numerically computed to confirm further complexity of these dynamics induced by the seasonal forcing on the mosquitoes oviposition rates. The obtained results show that ordinary differential equation models with external forcing can have rich dynamic behaviour, ranging from bifurcation to strange attractors which may explain the observed fluctuations found in RVF empiric outbreak data, as well as the non deterministic nature of RVF inter-epidemic activities. Furthermore, the coexistence of the endemic equilibrium is subjected to existence of certain number of infected Aedes mosquitoes, suggesting that Aedes have potential to initiate RVF epidemics through transovarial transmission and to sustain low levels of the disease during post epidemic periods. Therefore we argue that locations that may serve as RVF virus reservoirs should be eliminated or kept under control to prevent multi-periodic outbreaks and consequent chains of infections. The epidemiological significance of this study is: (1) low levels of birth rate (in both Aedes and Culex) can trigger unpredictable outbreaks; (2) Aedes mosquitoes are more likely capable of inducing unpredictable behaviour compared to the Culex; (3) higher oviposition rates on mosquitoes do not in general imply manifestation of irregular behaviour on the dynamics of the disease. Finally, our model with external seasonal forcing on vector oviposition rates is able to mimic the linear increase in livestock seroprevalence during inter-epidemic period showing a constant exposure and presence of active transmission foci. This suggests that RVF outbreaks partly build upon RVF inter-epidemic activities. Therefore, active RVF surveillance in livestock is recommended.