Vector-borne plant diseases represent a complex phytosanitary challenge. Mathematical models serve as a key tool for analyzing integrated management strategies, enabling more effective control of these pests. A dynamical system is presented to model the infection of Tahiti lime (Citrus x latifolia) with the bacterium Candidatus Liberibacter asiaticus (CLas), transmitted mainly by infected adults of the psyllid D. citri, which causes the citrus greening—Huanglongbing (HLB). The proposed model is based on the D. citri-HLB pathosystem, basic interactions between bacteria, vector psyllid hosts, trees and a vector parasitoid wasp. It consists of nine ordinary differential equations that model the rates of change of the numbers of infected and uninfected vector nymphs and adult females, of infected and uninfected trees of high and low productivity, and of the parasitoid Tamarixia radiata, recommended for the biological control of D. citri. The parameters of the model are identified from extant literature or otherwise estimated, in both cases being adjusted to Colombian conditions. A mathematical analysis of a simplified model is carried out, and simulations are conducted to demonstrate the effect of different types of control easures.

Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model was proposed to integrate phenotypic evolution, microenvironmental acidification, and tumor density dynamics. Three key mechanisms were incorporated in it: frequency-dependent selection favoring acid-resistant cells below a critical pH, stress-induced phenotypic switching, and a positive feedback loop where resistant cells produce excess acid that intensifies selection pressure. The well-posedness of the model was established. Through numerical simulations across biologically relevant parameter regimes, we identified two therapeutically targetable parameters: the baseline acid clearance rate (a proxy for vascular perfusion) and a protection factor (representing acid-resistance "machinery" effectiveness) as critical bifurcation parameters for resistance evolution. The model exhibits qualitatively distinct dynamics depending on phenotypic plasticity levels. In low-plasticity tumors, both parameters exhibit sharp bifurcations with strong parameter interactions: clearance and protection effects are context-dependent, with therapeutic interventions effective only within specific parameter ranges. In high-plasticity tumors, both parameters produce continuous, monotonic responses with independent, additive effects. These regime-dependent dynamics suggest that treatment strategies should adapt to tumor plasticity: in the former, targeting perfusion alone is typically sufficient, though sequential therapy may be required if the perfusion rate approaches or exceeds the bifurcation threshold, whereas in the latter, treatment might benefit from combination therapies addressing both parameters simultaneously. These findings suggest that a low-dimensional model can identify therapeutically targetable parameters governing resistance evolution, suggesting interventions that may prevent or reverse the harmful effect of acid-resistant phenotypes, which are associated with chemotherapy failure, immune evasion, and metastatic progression.

We constructed a compartmental mathematical model to study the dynamics of viral sexually transmitted infections (STIs) in a population consisting of men and women who engage in sexual contact with both sexes. Each sex is further split into compartments of susceptible, infected/infectious, and recovered/immune individuals, with constant per capita recovery and loss of immunity rates, while the per capita infection rates for each sex (force of infection) are based on standard incidence terms corresponding to the probabilities that the sexual partner of each sex that a susceptible individual randomly selects is an infected one. We explored possible effects of behavioral interventions, such as condom usage and reducing the number of sexual partnerships as well as the different dynamics of STI transmission between populations engaging solely in opposite-sex interactions and those engaging in non-opposite-sex interactions. These findings can help inform the development of public health policies aimed at alleviating the burden of sexually transmitted diseases.