A wide range of insects affect crop production and cause considerable yield losses. Difficulties reside on the development and adaptation of adequate strategies to predict insect pests for their timely management to ensure enhanced agricultural production. Several conceptual modelling frameworks have been proposed, and the choice of an approach depends largely on the objective of the model and the availability of data. This paper presents a summary of decades of advances in insect population dynamics, phenology models, distribution and risk mapping. Existing challenges on the modelling of insects are listed; followed by innovations in the field. New approaches include artificial neural networks, cellular automata (CA) coupled with fuzzy logic (FL), fractal, multi-fractal, percolation, synchronization and individual/agent-based approaches. A concept for assessing climate change impacts and providing adaptation options for agricultural pest management independently of the United Nations Intergovernmental Panel on Climate Change (IPCC) emission scenarios is suggested. A framework for estimating losses and optimizing yields within crop production system is proposed and a summary on modelling the economic impact of pests control is presented. The assessment shows that the majority of known insect modelling approaches are not holistic; they only concentrate on a single component of the system, i.e. the pest, rather than the whole crop production system. We suggest system thinking as a possible approach for linking crop, pest, and environmental conditions to provide a more comprehensive assessment of agricultural crop production

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. 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. 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. 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.

Rift Valley fever (RVF) outbreaks are recurrent, occurring at irregular intervals of up to 15 years at least in East Africa. Between outbreaks disease inter-epidemic activities exist and occur at low levels and are maintained by female Aedes mcintoshi mosquitoes which transmit the virus to their eggs leading to disease persistence during unfavourable seasons. Here we formulate and analyse a full stochastic host-vector model with two routes of transmission: vertical and horizontal. By applying branching process theory we establish novel relationships between the basic reproduction number, R₀, vertical transmission and the invasion and extinction probabilities. Optimum climatic conditions and presence of mosquitoes have not fully explained the irregular oscillatory behaviour of RVF outbreaks. Using our model without seasonality and applying van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how outbreaks multi-year periodicity varies with the vertical transmission. Our theory predicts complex fluctuations with a dominant period of 1 to 10 years which essentially depends on the efficiency of vertical transmission. Our predictions are then compared to temporal patterns of disease outbreaks in Tanzania, Kenya and South Africa. Our analyses show that interaction between nonlinearity, stochasticity and vertical transmission provides a simple but plausible explanation for the irregular oscillatory nature of RVF outbreaks. Therefore, we argue that while rainfall might be the major determinant for the onset and switch-off of an outbreak, the occurrence of a particular outbreak is also a result of a build up phenomena that is correlated to vertical transmission efficiency. Rift Valley fever (RVF) is a relatively novel vector-borne zoonotic disease, with long and irregular periods between outbreaks. Although outbreaks are highly correlated with occurrence of abnormal rainfall and flooding regimes, there have been instances with above normal rainfall where no disease outbreaks were recorded. This suggests that while rainfall might be the major determinant for the onset and switch-off of an outbreak, it may not be the only factor responsible for the temporal characteristic pattern of RVF outbreaks. We suspect that apart from influence of environmental conditions, disease outbreaks result from build up phenomena that depend on vertical transmission efficiency. Therefore, in this study we focus on formulating a stochastic host-vector model with two routes of transmission (horizontal and vertical) without seasonality to investigate the role of vertical transmission in the dynamics of the disease. First we apply branching process theory to characterize the relationships between vertical transmission and invasion probability and between vertical transmission and extinction probability. Finally, we apply an analytic approach, van Kampen’s system size expansion method to characterize disease complex fluctuations that are simply a result of interaction between demographic stochasticity, non-linearity and vertical transmission efficiency. Our results show that it is possible to reduce the frequency and intensity of RVF outbreaks by simply reducing the efficiency of vertical transmission.

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.

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.