From an experimental point of view, it is difficult to investigate the propagation mechanism of infectious disease and predict its trend. However, applying a nonlinear model offers a more straightforward and effective approach for analyzing transmission characteristics of infectious diseases. This paper proposes an SLVEIMQR dynamic model by dividing the population into susceptible (S), low-risk (L), vaccinated (V), exposed (E), infected (I), mutant (M), quarantined (Q) and recovered (R). The basic reproduction number and the equilibrium of the proposed model are computed, and the local asymptotic stability of the disease-free equilibrium is proved. Furthermore, the transcritical bifurcation at equilibrium and the sensitivity of key parameters are analyzed. To estimate the model parameters and predict the trend of infectious disease, the least squares method is applied by using epidemic data from different phases in Italy. The results show that the average relative errors of the model in the two prediction stages are 1.72% and 3.66%, respectively.
This study investigates a discrete nonlinear resource-effort system with a state-dependent carrying capacity, where the maximum exploitation capacity adapts to resource availability. Unlike classical fixed-capacity models, the proposed framework incorporates adaptive feedback between resource and exploitation variables, providing a generalized approach for analyzing complex dynamics in nonlinear discrete systems. Using the method of piecewise constant argument, the continuous model is transformed into a nonlinear discrete map. Fundamental properties, including positivity, boundedness, equilibrium points and local stability, are analyzed. The loss of stability at the interior equilibrium is explored through flip and Neimark–Sacker bifurcations, leading to period-doubling cascades, quasiperiodic oscillations and chaos. Normal form theory is applied to determine bifurcation direction and stability. Numerical simulations using bifurcation diagrams, phase portraits, time series and maximum Lyapunov exponents confirm complex transitions. A feedback control strategy is further proposed to stabilize unstable dynamics and enlarge the stability region.
We formulate and analyse a mathematical model for the within-host co-infection dynamics of Zika virus (ZIKV) and chikungunya virus (CHIKV), incorporating latently infected cells and cytotoxic T lymphocyte (CTL) immune responses. We establish the nonnegativity and boundedness of solutions. Using the next-generation matrix method, we derive the basic reproduction numbers ([Formula: see text]) and ([Formula: see text]) for the ZIKV and CHIKV submodels, respectively, and the overall reproduction number ([Formula: see text]). Invasion reproduction numbers, ([Formula: see text]) and ([Formula: see text]), are derived to characterise the ability of either virus to invade an established infection. Global stability of the equilibria is established using Lyapunov functions. We investigate three therapeutic protocols: antiviral treatment blocking viral entry, treatment reducing viral production, and IL-2 therapy enhancing CTL responses. Sensitivity analysis of ([Formula: see text]) and ([Formula: see text]) is performed, and numerical simulations support the stability results. Simulations indicate that combined antiviral and immune-based interventions suppress co-infection by reducing viral replication and enhancing immune-mediated clearance.
Pine wilt disease is a destructive forest disease involving pine trees, pinewood nematodes, and insect vectors. This study develops deterministic and stochastic delayed host–vector models to examine waiting periods and variability in transmission. For the deterministic system, positivity, boundedness, equilibria, and the basic reproduction number [Formula: see text] are established. The disease-free equilibrium is locally and globally asymptotically stable when [Formula: see text], while the endemic equilibrium is assessed through delay-dependent local stability. The stochastic model includes multiplicative environmental noise and is shown to possess positive solutions with bounded first moments. Exact Itô logarithmic identities demonstrate that long-term infection behaviour depends on current and delayed host–vector states. A delay-aware stochastic nonstandard finite difference scheme is constructed using delayed indices, nonstandard denominator functions, and positive stochastic exponential factors. Numerical experiments illustrate the effects of delay, noise, and step size, with the proposed scheme showing controlled behaviour at larger steps.
This paper establishes a state-feedback control system based on a nonlinear incidence SIRS model to explore the regulatory mechanism of infectious disease control. We develop a state-dependent impulsive model with threshold-triggered vaccination and isolation interventions once the susceptible population exceeds a predefined level. After investigating the basic properties of the ODE subsystem, we define and classify the Poincar & eacute; map and analyze its domain, range and monotonicity, which provides a theoretical basis for studying positive periodic solutions of the impulsive system under different ODE dynamics. The results show that the disease-free periodic solution is globally asymptotically stable for p > 1 , where p is a parameter directly related to the force of the infection. When 0 < p < 1, however, the model may exhibit bistability between the disease-free periodic solution and an endemic periodic solution, where the final outcome depends sensitively on the initial infection size, which is consistent with the weak transmissibility and controllable low-level prevalence.
