Mathematical models are a powerful method to understand and control the spread of Huanglongbing

Optimizing control parameters for Huanglongbing disease in citrus orchards using SAIR-SI compartmental model, epidemic final size, and genetic algorithms

Huanglongbing (HLB) is a bacterial disease that affects citrus trees worldwide. We present an innovative approach for identifying optimal control and risk measures for HLB in citrus orchards. Our method is based on a mathematical model that incorporates the number of roguing trees and a logistic growth model for the dynamic of the Asian Citrus Psyllid (ACP), the primary vector for HLB transmission. We derive an expression for: (1) the basic reproduction number R 0 ; (2) the final size for the number of roguing trees; and (3) the transmission risk. The above let us propose a difference map equation that assesses this final size with a low computational cost. We use this difference map in an evolutionary algorithm to identify the most effective combination of control parameter values for reducing HLB transmission, including the timing and frequency of roguing and the use of insecticides. In this sense, we propose two control strategies, which we called tree-centered and vector-centered.

Economical-epidemiological analysis of the coffee trees rust pandemic

Coffee leaf rust is a prevalent botanical disease that causes a worldwide reduction in coffee supply and its quality, leading to immense economic losses. While several pandemic intervention policies (PIPs) for tackling this rust pandemic are commercially available, they seem to provide only partial epidemiological relief for farmers. In this work, we develop a high-resolution spatiotemporal economical-epidemiological model, extending the Susceptible-Infected-Removed model, that captures the rust pandemic's spread in coffee tree farms and its associated economic impact. Through extensive simulations for the case of Colombia, a country that consists mostly of small-size coffee farms and is the second-largest coffee producer in the world, our results show that it is economically impractical to sustain any profit without directly tackling the rust pandemic. Furthermore, even in the hypothetical case where farmers perfectly know their farm's epidemiological state and the weather in advance, any rust pandemic-related efforts can only amount to a limited profit of roughly 4% on investment. In the more realistic case, any rust pandemic-related efforts are expected to result in economic losses, indicating that major disturbances in the coffee market are anticipated.

Modeling Study of the Effects of Ageratum conyzoides on the Transmission and Control of Citrus Huanglongbing

Ageratum conyzoides (A. conyzoides) is commonly found or intentionally planted in citrus orchards due to its ability to provide habitat and breeding grounds for the natural enemies of citrus pests. This study aims to expand from a switching Huanglongbing model by incorporating the effects of A. conyzoides, vector preferences for settling, and pesticide application intervals on disease transmission. Additionally, we establish the basic reproduction number R0 and its calculation for a general switching compartmental epidemic model. Theoretical findings demonstrate that the basic reproduction number serves as a threshold parameter to characterize the dynamics of the models: if R0<1, the disease will disappear, whereas if R0>1, it will spread. Numerical results indicate that the recruitment rate of A. conyzoides not only affects the spread speed of Huanglongbing but also leads to paradoxical effects. Specifically, in cases of high infection rates, a low recruitment rate of A. conyzoides can result in a decrease, rather than an increase, in the basic reproduction number. Conversely, a high recruitment rate can accelerate the spread of Huanglongbing. Furthermore, we show how different vector bias and pesticide spraying periods affect the basic reproduction number.

A soil water indicator for a dynamic model of crop and soil water interaction

Water scarcity is a critical issue in agriculture, and the development of reliable methods for determining soil water content is crucial for effective water management. This study proposes a novel, theoretical, non-physiological indicator of soil water content obtained by applying the next-generation matrix method, which reflects the water-soil-crop dynamics and identifies the minimum viable value of soil water content for crop growth. The development of this indicator is based on a two-dimensional, nonlinear dynamic that considers two different irrigation scenarios: the first scenario involves constant irrigation, and the second scenario irrigates in regular periods by assuming each irrigation as an impulse in the system. The analysis considers the study of the local stability of the system by incorporating parameters involved in the water-soil-crop dynamics. We established a criterion for identifying the minimum viable value of soil water content for crop growth over time. Finally, the model was calibrated and validated using data from an independent field study on apple orchards and a tomato crop obtained from a previous field study. Our results suggest the advantages of using this theoretical approach in modeling the plants' conditions under water scarcity as the first step before an empirical model. The proposed indicator has some limitations, suggesting the need for future studies that consider other factors that affect soil water content.

Modelling the spread and mitigation of an emerging vector-borne pathogen: Citrus greening in the U.S

Predictive models, based upon epidemiological principles and fitted to surveillance data, play an increasingly important role in shaping regulatory and operational policies for emerging outbreaks. Data for parameterising these strategically important models are often scarce when rapid actions are required to change the course of an epidemic invading a new region. We introduce and test a flexible epidemiological framework for landscape-scale disease management of an emerging vector-borne pathogen for use with endemic and invading vector populations. We use the framework to analyse and predict the spread of Huanglongbing disease or citrus greening in the U.S. We estimate epidemiological parameters using survey data from one region (Texas) and show how to transfer and test parameters to construct predictive spatio-temporal models for another region (California). The models are used to screen effective coordinated and reactive management strategies for different regions.

Role of vector resistance and grafting infection in Huanglongbing control models

Citrus huanglongbing (HLB) is one of the most devastating diseases affecting citrus almost worldwide due to the lack of a cure. To better understand the impact of insecticide resistance and grafting infection on the spread of HLB disease, a vector-borne compartmental model is formulated to describe the transmission dynamics of HLB between citrus and Asian citrus psyllid (ACP). The basic reproduction number R₀ is computed by using the next generation matrix approach, which is a threshold value of the uniform persistence and disappearance of HLB disease. By applying the sensitivity analysis of R₀, we obtain some parameters with the most significant influence on the transmission dynamics of HLB. Moreover, we also obtain that grafting infection has the least influence on the transmission dynamics of HLB. Additionally, a time-dependent control model of HLB to minimize the cost of implementing control efforts and infected trees and ACPs is formulated. By using Pontryagin's Minimum Principle, we obtain the optimal integrated strategy and prove the uniqueness of optimal control solution. The simulation results illustrate that the strategy involving two time-dependent optimal controls is the most effective to suppress the spread of the disease. However, insecticide spraying is more effective measure compared with infected tree removing.

Modeling and analysis of novel COVID-19 outbreak under fractal-fractional derivative in Caputo sense with power-law: a case study of Pakistan

In this paper, a five-compartment model is used to explore the dynamics of the COVID-19 pandemic, taking the vaccination campaign into account. The present model consists of five components that lead to a system of five ordinary differential equations. In this paper, we examined the disease from the perspective of a fractal fractional derivative in the Caputo sense with a power law type kernal. The model is also fitted with real data for Pakistan between June 1, 2020, and March 8, 2021. The fundamental mathematical characteristics of the model have been investigated thoroughly. We have calculated the equilibrium points and the reproduction number for the model and obtained the feasible region for the system. The existence and stability criteria of the model have been validated using the Banach fixed point theory and the Picard successive approximation technique. Furthermore, we have conducted stability analysis for both the disease-free and endemic equilibrium states. On the basis of sensitivity analysis and the dynamics of the threshold parameter, we have estimated the effectiveness of vaccination and identified potential control strategies for the disease using the proposed model outbreaks. The stability of the concerned solution in Ulam-Hyers and Ulam-Hyers-Rassias sense is also investigated. For the proposed problem, some results regarding basic reproduction numbers and stability analysis for various parameters are represented graphically. Matlab software is used for numerical illustrations. Graphical representations are given for different fractional orders and for various parametric values.

Modelling the temperature suitability for the risk of West Nile Virus establishment in European Culex pipiens populations

Increases in temperature and extreme weather events due to global warming can create an environment that is beneficial to mosquito populations, changing and possibly increasing the suitable geographical range for many vector-borne diseases. West Nile Virus (WNV) is a flavivirus, maintained in a mosquito-avian host cycle that is usually asymptomatic but can cause primarily flu-like symptoms in human and equid accidental hosts. In rare circumstances, serious disease and death are possible outcomes for both humans and horses. The main European vector of WNV is the Culex pipiens mosquito. This study examines the effect of environmental temperature on WNV establishment in Europe via Culex pipiens populations through use of a basic reproduction number ( R 0 ${R_0}$ ) model. A metric of thermal suitability derived from R 0 ${R_0}$ was developed by collating thermal responses of different Culex pipiens traits and combining them through use of a next-generation matrix. WNV establishment was determined to be possible between 14°C and 34.3°C, with the optimal temperature at 23.7°C. The suitability measure was plotted against monthly average temperatures in 2020 and the number of months with high suitability mapped across Europe. The average number of suitable months for each year from 2013 to 2019 was also calculated and validated with reported equine West Nile fever cases from 2013 to 2019. The widespread thermal suitability for WNV establishment highlights the importance of European surveillance for this disease and the need for increased research into mosquito and bird distribution.

Global dynamics and bifurcation analysis of an insect-borne plant disease model with two transmission routes

Huanglongbing (HLB) is a plant disease mainly spread by the insect-borne citrus psyllid. It is the most destructive citrus pathosystem worldwide. To understand the impact of sexual transmission on HLB dynamics, we propose a host–vector–HLB compartment model incorporating two transmission routes. The basic reproduction number [Formula: see text] is derived. Various interventions of the disease are assessed. We also investigate the effect of different incidence functions to simulate sexual transmission. For the case of sublinear incidence functions, the disease-free equilibrium is globally asymptotically stable (GAS) provided [Formula: see text]. For mass action incidence of sexual transmission, the endemic equilibrium is GAS provided [Formula: see text]. However, under nonlinear incidence, it is proved that the model may exhibit backward bifurcation. Theoretical and numerical studies reveal that (i) different forces of infection between heterosexual psyllids in the model may have a distinct impact on disease dynamics; (ii) sensitivity analysis shows that for [Formula: see text], the transmission rate between host and vector is more sensitive parameter than that between heterosexual psyllids; (iii) if the sexual transmission is ignored, the disease burden is likely to be underestimated in comparison with realistic scenarios; (iv) in the absence of chemical insecticides, the combined use of yellow sticky traps and injection of nutrient solutions can be more effective in suppressing the spread of HLB. These findings provide valuable insights for public policymakers to determine the long-term viability of implemented HLB management strategies and highlight the urgency of finding sustainable HLB solutions.

Bifurcation and optimal control analysis of delayed models for huanglongbing

In this paper, a delayed differential model of citrus Huanglongbing infection is analyzed, in which the latencies of the citrus tree and Asian citrus psyllid are considered as two time delay factors. We compute the equilibrium points and the basic reproductive numbers with and without time delays, i.e. [Formula: see text] and [Formula: see text], and then show that [Formula: see text] completely determines the local stability of the disease-free equilibrium. Moreover, the conditions for the existence of transcritical bifurcation are derived from Sotomayor’s Theorem. The stability of the endemic equilibrium and the existence of Hopf bifurcation are investigated in four cases: (1) [Formula: see text], (2) [Formula: see text], (3) [Formula: see text] and (4) [Formula: see text]. Optimal control theory is then applied to the model to study two time-dependent treatment efforts and minimize the infection in citrus and psyllids, while keeping the implementation cost at a minimum. Numerical simulations of the overall systems are implemented in MatLab for demonstration of the theoretical results.

Predicting temperature-dependent transmission suitability of bluetongue virus in livestock

The transmission of vector-borne diseases is governed by complex factors including pathogen characteristics, vector–host interactions, and environmental conditions. Temperature is a major driver for many vector-borne diseases including Bluetongue viral (BTV) disease, a midge-borne febrile disease of ruminants, notably livestock, whose etiology ranges from mild or asymptomatic to rapidly fatal, thus threatening animal agriculture and the economy of affected countries. Using modeling tools, we seek to predict where the transmission can occur based on suitable temperatures for BTV. We fit thermal performance curves to temperature-sensitive midge life-history traits, using a Bayesian approach. We incorporate these curves into S(T), a transmission suitability metric derived from the disease’s basic reproductive number, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0.$$\end{document}R0. This suitability metric encompasses all components that are known to be temperature-dependent. We use trait responses for two species of key midge vectors, Culicoides sonorensis and Culicoides variipennis present in North America. Our results show that outbreaks of BTV are more likely between 15\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}∘ C and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$34^{\circ }\hbox { C}$$\end{document}34∘C, with predicted peak transmission risk at 26 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ$$\end{document}∘ C. The greatest uncertainty in S(T) is associated with the following: the uncertainty in mortality and fecundity of midges near optimal temperature for transmission; midges’ probability of becoming infectious post-infection at the lower edge of the thermal range; and the biting rate together with vector competence at the higher edge of the thermal range. We compare three model formulations and show that incorporating thermal curves into all three leads to similar BTV risk predictions. To demonstrate the utility of this modeling approach, we created global suitability maps indicating the areas at high and long-term risk of BTV transmission, to assess risk and to anticipate potential locations of disease establishment.

Huanglongbing Model under the Control Strategy of Discontinuous Removal of Infected Trees

By using differential equations with discontinuous right-hand sides, a dynamic model for vector-borne infectious disease under the discontinuous removal of infected trees was established after understanding the transmission mechanism of Huanglongbing (HLB) disease in citrus trees. Through calculation, the basic reproductive number of the model can be attained and the properties of the model are discussed. On this basis, the existence and global stability of the calculated equilibria are verified. Moreover, it was found that different I0 in the control strategy cannot change the dynamic properties of HLB disease. However, the lower the value of I0, the fewer HLB-infected citrus trees, which provides a theoretical basis for controlling HLB disease and reducing expenditure.

Reproduction number and sensitivity analysis of cassava mosaic disease spread for policy design

We develop a mathematical model for the dynamics of Cassava Mosaic Disease (CMD), which is driven by both planting of infected cuttings and whitefly transmission. We use the model to analyze the dynamics of a CMD outbreak and to identify the most cost-effective policy for controlling it. The model uses the reproduction number $ \mathscr{R}_0 $ as a threshold, calculated using the Next-Generation Method. A locally-asymptotically-stable disease-free equilibrium is established when $ \mathscr{R}_0 < 1 $, proved by the Routh-Hurwitz criterion. The globally-asymptotically-stable disease-free and endemic-equilibrium points are obtained using Lyapunov's method and LaSalle's invariance principle. Our results indicate that the disease-free equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 \leq 1 $, while the endemic-equilibrium point is globally-asymptotically-stable when $ \mathscr{R}_0 > 1 $. Our sensitivity analysis shows that $ \mathscr{R}_0 $ is most sensitive to the density of whitefly. Numerical simulations confirmed the effectiveness of whitefly control for limiting an outbreak while minimizing costs.

Analysis and optimal control of a Huanglongbing mathematical model with resistant vector

Huanglongbing (HLB) is an incurable disease that affects citrus trees. To better understand the transmission of HLB, the mathematical model is developed to investigate the transmission dynamics of the disease between Asian citrus psyllid (ACP) and citrus trees. Through rigorous mathematical derivations, we derive the expression of the basic reproduction number (R₀) of HLB. The findings show that the disease-free equilibrium is locally asymptotically stable if R₀ < 1, and if R₀ > 1 the system is uniformly persistent. By applying the global sensitivity analysis of R₀, we can obtain some parameters that have the greatest influence on the HLB transmission dynamics. Additionally, the optimal control theory is used to explore the corresponding optimal control problem of the HLB model. Numerical simulations are conducted to reinforce the analytical results. These theoretical and numerical results provide useful insights for understanding the transmission dynamics of HLB and may help policy makers to develop intervention strategies for the disease.

Transmission dynamics and optimal control of a Huanglongbing model with time delay

In this paper, a mathematical model has been formulated for the transmission dynamics of citrus Huanglongbing considering latent period as the time delay factor. Existence of the equilibria and their stability have been studied on the basis of basic reproduction number in two cases τ=0 and τ>0. The results show that stability changes occur through Hopf bifurcation in the delayed system. Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using three time-dependent control variables determined from sensitivity analysis. By using Pontryagin's Maximum Principle, we obtain the optimal integrated strategy and prove the uniqueness of optimal control solution. Analytical and numerical findings suggest that it is feasible to implement control techniques while minimizing the cost of implementation of optimal control strategies.

Understanding how temperature shifts could impact infectious disease

Climate change is expected to have complex effects on infectious diseases, causing some to increase, others to decrease, and many to shift their distributions. There have been several important advances in understanding the role of climate and climate change on wildlife and human infectious disease dynamics over the past several years. This essay examines 3 major areas of advancement, which include improvements to mechanistic disease models, investigations into the importance of climate variability to disease dynamics, and understanding the consequences of thermal mismatches between host and parasites. Applying the new information derived from these advances to climate-disease models and addressing the pressing knowledge gaps that we identify should improve the capacity to predict how climate change will affect disease risk for both wildlife and humans.

Effect of Daytime and Tree Canopy Height on Sampling of Cacopsylla melanoneura, a 'Candidatus Phytoplasma mali' Vector

The psyllids Cacopsylla melanoneura and Cacopsylla picta reproduce on apple (Malus × domestica) and transmit the bacterium ‘Candidatus Phytoplasma mali’, the causative agent of apple proliferation. Adult psyllids were collected by the beating-tray method from lower and upper parts of the apple tree canopy in the morning and in the afternoon. There was a trend of catching more emigrant adults of C.melanoneura in the morning and in the lower part of the canopy. For C.melanoneura remigrants, no differences were observed. The findings regarding the distribution of adults were reflected by the number of nymphs collected by wash-down sampling. The density of C.picta was too low for a statistical analysis. The vector monitoring and how it is commonly performed, is suitable for estimating densities of C.melanoneura. Nevertheless, above a certain temperature threshold, prediction of C.melanoneura density might be skewed. No evidence was found that other relatively abundant psyllid species in the orchard, viz. Baeopelma colorata, Cacopsylla breviantennata, Cacopsylla brunneipennis, Cacopsylla pruni and Trioza urticae, were involved in ‘Candidatus Phytoplasma mali’ transmission. The results of our study contribute to an advanced understanding of insect vector behavior and thus have a practical impact for an improved field monitoring.

Linking metabolic phenotypes to pathogenic traits among "Candidatus Liberibacter asiaticus" and its hosts

Candidatus Liberibacter asiaticus (CLas) has been associated with Huanglongbing, a lethal vector-borne disease affecting citrus crops worldwide. While comparative genomics has provided preliminary insights into the metabolic capabilities of this uncultured microorganism, a comprehensive functional characterization is currently lacking. Here, we reconstructed and manually curated genome-scale metabolic models for the six CLas strains A4, FL17, gxpsy, Ishi-1, psy62, and YCPsy, in addition to a model of the closest related culturable microorganism, L. crescens BT-1. Predictions about nutrient requirements and changes in growth phenotypes of CLas were confirmed using in vitro hairy root-based assays, while the L. crescens BT-1 model was validated using cultivation assays. Host-dependent metabolic phenotypes were revealed using expression data obtained from CLas-infected citrus trees and from the CLas-harboring psyllid Diaphorina citri Kuwayama. These results identified conserved and unique metabolic traits, as well as strain-specific interactions between CLas and its hosts, laying the foundation for the development of model-driven Huanglongbing management strategies.

Age influences the thermal suitability of Plasmodium falciparum transmission in the Asian malaria vector Anopheles stephensi

Models predicting disease transmission are vital tools for long-term planning of malaria reduction efforts, particularly for mitigating impacts of climate change. We compared temperature-dependent malaria transmission models when mosquito life-history traits were estimated from a truncated portion of the lifespan (a common practice) versus traits measured across the full lifespan. We conducted an experiment on adult female Anopheles stephensi, the Asian urban malaria mosquito, to generate daily per capita values for mortality, egg production and biting rate at six constant temperatures. Both temperature and age significantly affected trait values. Further, we found quantitative and qualitative differences between temperature-trait relationships estimated from truncated data versus observed lifetime values. Incorporating these temperature-trait relationships into an expression governing the thermal suitability of transmission, relative R₀(T), resulted in minor differences in the breadth of suitable temperatures for Plasmodium falciparum transmission between the two models constructed from only An. stephensi trait data. However, we found a substantial increase in thermal niche breadth compared with a previously published model consisting of trait data from multiple Anopheles mosquito species. Overall, this work highlights the importance of considering how mosquito trait values vary with mosquito age and mosquito species when generating temperature-based suitability predictions of transmission.

The Role of Vector Trait Variation in Vector-Borne Disease Dynamics

Many important endemic and emerging diseases are transmitted by vectors that are biting arthropods. The functional traits of vectors can affect pathogen transmission rates directly and also through their effect on vector population dynamics. Increasing empirical evidence shows that vector traits vary significantly across individuals, populations, and environmental conditions, and at time scales relevant to disease transmission dynamics. Here, we review empirical evidence for variation in vector traits and how this trait variation is currently incorporated into mathematical models of vector-borne disease transmission. We argue that mechanistically incorporating trait variation into these models, by explicitly capturing its effects on vector fitness and abundance, can improve the reliability of their predictions in a changing world. We provide a conceptual framework for incorporating trait variation into vector-borne disease transmission models, and highlight key empirical and theoretical challenges. This framework provides a means to conceptualize how traits can be incorporated in vector borne disease systems, and identifies key areas in which trait variation can be explored. Determining when and to what extent it is important to incorporate trait variation into vector borne disease models remains an important, outstanding question.

What makes or breaks a campaign to stop an invading plant pathogen?

Diseases in humans, animals and plants remain an important challenge in our society. Effective control of invasive pathogens often requires coordinated concerted action of a large group of stakeholders. Both epidemiological and human behavioural factors influence the outcome of a disease control campaign. In mathematical models that are frequently used to guide such campaigns, human behaviour is often ill-represented, if at all. Existing models of human, animal and plant disease that do incorporate participation or compliance are often driven by pay-offs or direct observations of the disease state. It is however very well known that opinion is an important driving factor of human decision making. Here we consider the case study of Citrus Huanglongbing disease (HLB), which is an acute bacterial disease that threatens the sustainability of citrus production across the world. We show how by coupling an epidemiological model of this invasive disease with an opinion dynamics model we are able to answer the question: What makes or breaks the effectiveness of a disease control campaign? Frequent contact between stakeholders and advisors is shown to increase the probability of successful control. More surprisingly, we show that informing stakeholders about the effectiveness of control methods is of much greater importance than prematurely increasing their perceptions of the risk of infection. We discuss the overarching consequences of this finding and the effect on human as well as plant disease epidemics.

The successful regional control of emerging and invasive diseases often requires that a sufficiently large proportion of the population comply with the control strategy. This is notably the case in diseases such as measles but also applies to epidemics in animals and plants. If insufficient numbers of stakeholders comply with disease control, or if control becomes uncoordinated for some reason, then control fails. Therefore, both epidemiological and human behavioural factors influence the outcome of emerging, endemic, and invasive disease control campaigns. Mathematical models are often used to determine factors that are important for disease control to be successful, but these models tend to focus on the epidemiology and efficacy of control, frequently neglecting human behaviour. A number of mathematical models of human disease, and to some extent animal disease do incorporate participation or compliance behaviours; however, studies looking at human actions and attitudes towards plant disease control are quite rare and almost exclusively driven by pay-offs or direct observations of the disease state. It is however very well known that opinion, for example about how effective control is perceived to be, is also a key driving factor of human decision making. Here we consider the case study of Citrus Huanglongbing disease (HLB), a devastating invasive disease in citrus which threatens production worldwide. We show how by coupling an epidemiological model with an opinion dynamics model it is possible to answer the question: What makes or breaks the effectiveness of a disease control campaign?

Modeling Temperature Effects on Population Density of the Dengue Mosquito Aedes aegypti

Mosquito density plays an important role in the spread of mosquito-borne diseases such as dengue and Zika. While it remains very challenging to estimate the density of mosquitoes, modelers have tried different methods to represent it in mathematical models. The goal of this paper is to investigate the various ways mosquito density has been quantified, as well as to propose a dynamical system model that includes the details of mosquito life stages leading to the adult population. We first discuss the mosquito traits involved in determining mosquito density, focusing on those that are temperature dependent. We evaluate different forms of models for mosquito densities based on these traits and explore their dynamics as temperature varies. Finally, we compare the predictions of the models to observations of Aedes aegypti abundances over time in Vitòria, Brazil. Our results indicate that the four models exhibit qualitatively and quantitatively different behaviors when forced by temperature, but that all seem reasonably consistent with observed abundance data.

Thermal biology of mosquito-borne disease

Mosquito-borne diseases cause a major burden of disease worldwide. The vital rates of these ectothermic vectors and parasites respond strongly and nonlinearly to temperature and therefore to climate change. Here, we review how trait-based approaches can synthesise and mechanistically predict the temperature dependence of transmission across vectors, pathogens, and environments. We present 11 pathogens transmitted by 15 different mosquito species - including globally important diseases like malaria, dengue, and Zika - synthesised from previously published studies. Transmission varied strongly and unimodally with temperature, peaking at 23-29ºC and declining to zero below 9-23ºC and above 32-38ºC. Different traits restricted transmission at low versus high temperatures, and temperature effects on transmission varied by both mosquito and parasite species. Temperate pathogens exhibit broader thermal ranges and cooler thermal minima and optima than tropical pathogens. Among tropical pathogens, malaria and Ross River virus had lower thermal optima (25-26ºC) while dengue and Zika viruses had the highest (29ºC) thermal optima. We expect warming to increase transmission below thermal optima but decrease transmission above optima. Key directions for future work include linking mechanistic models to field transmission, combining temperature effects with control measures, incorporating trait variation and temperature variation, and investigating climate adaptation and migration.

Predicting the fundamental thermal niche of crop pests and diseases in a changing world: A case study on citrus greening

Predicting where crop pests and diseases can occur, both now and in the future under different climate change scenarios, is a major challenge for crop management. One solution is to estimate the fundamental thermal niche of the pest/disease to indicate where establishment is possible. Here, we develop methods for estimating and displaying the fundamental thermal niche of pests and pathogens and apply these methods to Huanglongbing (HLB), a vector-borne disease that is currently threatening the citrus industry worldwide.We derive a suitability metric based on a mathematical model of HLB transmission between tree hosts and its vector Diaphorina citri, and incorporate the effect of temperature on vectortraits using data from laboratory experiments performed at different temperatures. We validate the model using data on the historical range of HLB.Our model predicts that transmission of HLB is possible between 16 and 33°C with peak transmission at ~25°C. The greatest uncertainty in our suitability metric is associated with the mortality of the vectors at peak transmission, and fecundity at the edges of the thermal range, indicating that these parameters need further experimental work.We produce global thermal niche maps by plotting how many months each location is suitable for establishment of the pest/disease. This analysis reveals that the highest suitability for HLB occurs near the equator in large citrus-producing regions, such as Brazil and South-East Asia. Within the Northern Hemisphere, the Iberian peninsula and California are HLB suitable for up to 7 months of the year and are free of HLB currently.Policy implications. We create a thermal niche map which indicates the places at greatest risk of establishment should a crop disease or pest enter these regions. This indicates where surveillance should be focused to prevent establishment. Our mechanistic method can be used to predict new areas for Huanglongbing transmission under different climate change scenarios and is easily adapted to other vector-borne diseases and crop pests.

Detection and Seasonal Variations of Huanglongbing Disease in Navel Orange Trees Using Direct Ionization Mass Spectrometry

Citrus greening disease [Huanglongbing (HLB)] is the most destructive disease of citrus. In this work, we have established a metabolite-based mass spectrometry (MS) method for rapid detection of HLB in navel orange trees. Without sample pretreatment, characteristic mass spectra can be directly obtained from the raw plant samples using the direct MS method. The whole detection process can be accomplished within 1 min. By monitoring and comparisons of the healthy and infected plants throughout a whole year, characteristic MS peaks of metabolites are found to be specific responses from infected plants and, thus, could be used as biomarkers for detection of HLB. Therefore, HLB could be directly detected in the asymptomatic samples, such as stems, using this metabolite-based direct MS method. In addition, principal component analysis and partial least squares discriminant analysis modes of metabolites from healthy and infected trees were established for investigating differentiation and seasonal variations of HLB in leaves, veins, and stems, providing valuable information for understanding the HLB in different seasons.

Regional Spatial-Temporal Spread of Citrus Huanglongbing Is Affected by Rain in Florida

Citrus huanglongbing (HLB), associated with 'Candidatus Liberibacter asiaticus' (Las), disseminated by Asian citrus psyllid (ACP), has devastated citrus in Florida since 2005. Data on HLB occurrence were stored in databases (2005 to 2012). Cumulative HLB-positive citrus blocks were subjected to kernel density analysis and kriging. Relative disease incidence per county was calculated by dividing HLB numbers by relative tree numbers and maximum incidence. Spatiotemporal HLB distributions were correlated with weather. Relative HLB incidence correlated positively with rainfall. The focus expansion rate was 1626 m month^-1, similar to that in Brazil. Relative HLB incidence in counties with primarily large groves increased at a lower rate (0.24 year^-1) than in counties with smaller groves in hotspot areas (0.67 year^-1), confirming reports that large-scale HLB management may slow epidemic progress.