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

Flexible regression model for predicting the dissemination of Candidatus Liberibacter asiaticus under variable climatic conditions

Greening, or Huanglongbing (HLB), poses a severe threat to global citrus cultivation, affecting various citrus species and compromising fruit production. Primarily transmitted by psyllids during phloem feeding, the bacterium Candidatus Liberibacter induces detrimental symptoms, including leaf yellowing and reduced fruit quality. Given the limitations of conventional control strategies, the search for innovative approaches, such as resistant genotypes and early diagnostic methods, becomes essential for the sustainability of citrus cultivation. The development of predictive models, such as the one proposed in this study, is essential as it enables the estimation of the bacterium's concentration and the vulnerability of healthy plants to infection, which will be instrumental in determining the risk of HLB. This study proposes a prediction model utilizing environmental factors, including temperature, humidity, and precipitation, which play a decisive role in greening epidemiology, influencing the complex interaction among the pathogen, vector, and host plant. In the proposed modeling, it addresses non-linear relationships through cubic smoothing splines applications and tackles imbalanced categorical predictor variables, requiring the use of a random-effects regression model, incorporating a random intercept to account for variability across different groups and mitigate the risk of biased predictions. The model's ability to predict HLB incidence under varying climatic conditions provides a significant contribution to disease management, offering a strategic tool for early intervention and potentially reducing the spread of HLB. Using climatological and environmental data, the research aims to develop a predictive model, assessing the influence of these variables on the spread of Candidatus Liberibacter asiaticus, essential for effective disease management. The proposed flexible model demonstrates robust predictions for both training and test data, identifying climatological and environmental predictors influencing the dissemination of Candidatus Liberibacter asiaticus, the vascular bacterium associated with Huanglongbing (HLB) or greening.

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.

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.

Analysis and dynamical behavior of a novel dengue model via fractional calculus

The infection of dengue is an intimidating vector-borne disease caused by a pathogenic agent that affects different temperature areas and brings many losses in human health and economy. Thus, it is valuable to identify the most influential parameters in the transmission process for the control of dengue to lessen these losses and to turn down the economic burden of dengue. In this research, we formulate the transmission phenomena of dengue infection with vaccination, treatment and reinfection via Atangana–Baleanu operator to thoroughly explore the intricate system of the disease. Furthermore, to come up with more realistic, dependable and valid results through fractional derivative rather than classical order derivative. The next-generation approach has been utilized to compute the basic reproduction number for the suggested fractional model, indicated by [Formula: see text]; moreover, we conducted sensitivity test of [Formula: see text] to recognize and point out the role of parameters on [Formula: see text]. Our numerical results predict that the reproduction number of the system of dengue infection can be controlled by controlling the index of memory. The uniqueness and existence result has been proved for the solution of the system. A novel numerical method is presented to highlight the time series of dengue system. Eventually, we get numerical results for different assumptions of [Formula: see text] with specifying factors to conceptualize the effect of [Formula: see text] on the dynamics. It has been noted that the fractional-order derivative offers realistic, clear-cut and valid information about the dynamics of dengue fever. Moreover, we note through our analysis that the input parameters’ index of memory, biting rate, transmission probability and recruitment rate of mosquitos can be used as control parameter to lower the level of infection.