An SIRS (Susceptible-Infectious-Recovered-Susceptible) model with sexual structure and dual incubation delays was proposed to characterize the effects of homosexual and heterosexual behaviors on the transmission dynamics and optimal control of gonorrhea. First, the nonnegativity and boundedness of solutions were obtained, and the basic reproduction number R-0 was calculated as well. Second, local and global asymptotical stability of the disease-free equilibrium was established if R-0 < 1. If R-0 > 1 the disease was uniformly persistent, and there existed at least one endemic equilibrium. An optimal control strategy was derived based on sensitivity analysis and practical intervention policy. Finally, the theoretical findings were illustrated through numerical simulations, revealing that targeted management of male infected individuals can markedly diminish gonorrhea prevalence, while disregarding the incubation periods tended to substantially overestimate the epidemic scale.

In this paper, a virus suppressed and delayed immune impairment model is proposed to characterize the immunity mediated HIV infection dynamics, with virus-to-cell and cell-to-cell transmission routes. First, criteria on the existence and globally asymptotical stability of infection-free, immune-free and immune-activated infection equilibria are established. Saddle-node bifurcation on the immune-activated infection equilibrium is further detailedly discussed. Furthermore, criteria on the Hopf bifurcation with both inhibition and delay as bifurcation parameters are obtained either separately or simultaneously by crossing curves. Finally, the theoretical results are demonstrated by numerical simulations. We find that if immune suppression or delay is considered respectively, there would undergo Hopf bifurcation, while the simultaneous effect of both factors may lead to chaos. Meanwhile, the human immune system would become chaotic if the threshold value of virus suppression is always within a certain range, otherwise, the HIV infection would become controllable.

This study proposes a stochastic reaction-diffusion model for HIV/AIDS transmission to uncover the foundational mechanisms behind disease extinction and project the future trajectory of the pandemic. For the proposed model, we initially apply the idea of the Zvonkin transformation to establish a novel analytical framework. Subsequently, the existence and uniqueness of a globally positive solution were demonstrated by reformulating the problem within the context of a reaction-diffusion equation. Furthermore, we establish sufficient conditions for disease persistence by constructing an appropriate Lyapunov function. Within a specific parameter regime, we also prove that the disease becomes extinct at an exponential rate. More importantly, by leveraging the latest advances in long-acting antiretroviral therapy (LA-ART) and stochastic modeling theory, we derive the stationary distributions and probability density function for the theoretical zero mortality rate from AIDS-induced death. And, a series of numerical simulations is conducted to validate the theoretical findings. The simulation results confirm that a specific level of noise is sufficient to cause the disease to die out exponentially. Theoretical analysis predicts that AIDS will continue to pose a major public health threat, with its asymptomatic stage being a critical determinant of the disease's overall trajectory. Consequently, future efforts must prioritize this stage. A deeper investigation into its underlying mechanisms is essential to develop targeted interventions.

In this paper, a delayed two-strain patch SIS epidemic model is proposed with varying incidence and migration of susceptible individuals induced by media coverage of infected individuals. For the subsystem without migration, criteria on the globally asymptotical stability of disease-free equilibrium and Hopf bifurcations at the dominant and coexistent equilibria are established, where the global Hopf bifurcations are unbounded. For the model with migration, the basic reproduction number R-0 is derived, by which criteria on the locally and globally asymptotic stability of disease-free equilibrium are derived. The uniform persistence of (strain 1 or 2 dominant and coinfection) diseases is verified, respectively. The theoretical results are illustrated by numerical simulation, from which we find that R-0 is nonmonotonic with the migration rates between patches. Ignoring the multistrain factor will greatly underestimate the scale of disease, and even obtain the opposite conclusion (disease extinction or persistence). Delay could cause periodic oscillation, and the multistrain and migration between patches could further produce chaos. Both the media effect with delay and migration could greatly influence the transmission dynamics of disease from stability to instability and then to chaos, which would further increase the difficulty of disease control.

This paper introduces a novel class of delayed virus-to-cell HIV models incorporating general incidence and Logistic growth, with the objective of elucidating the complex reactivation dynamics of latently infected cells. Analytical results demonstrate that the HIV infection is cleared from the T-cells population when the basic reproduction number [Formula: see text]; if [Formula: see text], the criteria for local and global asymptotic stability of the endemic equilibrium are established under the condition that the death rate [Formula: see text] of target T-cells is greater than or equal to the intrinsic mitosis rate [Formula: see text]. Conversely, when [Formula: see text] is less than [Formula: see text], the system is shown to exhibit rich dynamical behaviors. Furthermore, the characteristic equation at endemic equilibrium with the coefficients dependent on two time delays is analyzed. Hopf bifurcation criteria are derived for both the general case, where both delays vary simultaneously as bifurcation parameters, and the special case involving only a single delay. The analyses reveal that stability switches can be induced, while chaotic phenomena emerge only when the delays become sufficiently large. Theoretical findings are validated through numerical simulations, which further indicate that a higher latency reactivation rate contributes to more effective control of HIV transmission. In contrast, a prolonged latent infection delay is ultimately predicted to precipitate a rapid viral load rebound.

This paper proposes a within-host Mycobacterium tuberculosis (Mtb) infection model integrating M1/M2 macrophage conversion to explore macrophage polarization regulation in pulmonary infection with cellular immunity. The basic reproduction number R0 is calculated, and criteria on the locally and globally asymptotic stability of infection-free equilibrium E0 are established if R0<1. Criteria on the existence and locally asymptotic stability of immune-free infection equilibrium E¯ and immune-activated infection equilibrium E∗ are further obtained if R0>1. Moreover, the model exhibits forward, backward and saddle-node bifurcations at E¯, as well as Hopf bifurcation and chaotic dynamics at E∗, indicating that Mtb infection is highly sensitive to the dynamic shifts during macrophage polarization. Numerical simulations verify theoretical results, revealing that the effective conversion rates γ1 and γ2 between M1 and M2 macrophages are key regulators of Mtb infection progression, which may provide theoretical insights into tuberculosis latency and relapse, and offer testable predictions for immunotherapeutic strategies.

In this paper, a reaction-diffusion SIR epidemic model with chemotaxis and delay is proposed to explore the completed dynamics, i.e., Turing and Hopf bifurcations and spatiotemporal inhomogeneous patterns. First, the basic reproduction number R0 is defined, and threshold criterion on the locally asymptotic stability of disease-free equilibrium is obtained. Second, the sufficient conditions on Turing bifurcation, Hopf bifurcation and Turing-Hopf bifurcation at the endemic equilibrium are obtained by taking delay and chemotaxis as bifurcation parameters respectively. It is proven that delay could induce Hopf bifurcation and chemotaxis could yield Turing bifurcation. Finally, the theoretical results and stable regions of endemic equilibrium with delay and chemotaxis are detailedly illustrated by numerical simulation. We find that complex spatiotemporal heterogeneous patterns could occur due to Hopf bifurcation-Turing instability, Hopf-Turing bifurcation or complex Hopf bifurcation, which could bring great challenges in disease prevention and control on each region with possible periodic outbreaks.

In this article, we investigate the dynamical behavior and asymptotic profiles for a host-pathogen epidemic model, where the different advection rates and degenerated heterogeneous diffusions are adopted and the total population is variable. First, the scalar equation of susceptible with diffusion d(S)(& sdot;) and advection rate qS is investigated. The existence, global stability and prior estimations of positive steady state are established, and then the asymptotic properties of positive steady state are discussed as d(S)(& sdot;) and qS approach to zero or infinity, respectively. Next, the well-posedness of solutions for the model, including the global existence, nonnegativity and ultimate boundedness of solutions, and the existence of global attractor are established. Following, the display expression of the basic reproduction number R-0 is calculated by means of the variational method. The local reproduction number R(& sdot;), the special forms R (0), R- 0, R- 0 of R-0 and the relationships between these reproduction numbers are presented. Then, the global dynamics of solutions for the model in terms with R0 are established by using the comparison principle, properties of principle eigenvalue and the persistence theory of dynamical systems. That is, when R-0 < 1, the disease-free steady state is globally asymptotic stable, otherwise when R-0 > 1, the disease is uniformly persistent. Furthermore, it is proved that R-0 is monotonically decreasing with respect to advection rate q(I )of infected individuals. The asymptotic profiles of R-0 in relation to the heterogeneous diffusion rates dS(& sdot;), dI (& sdot;) and advection rates q(S), q(I) approaching zero or infinity are discussed in detail by means of the display expression of R0 and the corresponding principal eigenvalue and weight eigenvalue problems, including the eighteen limit cases of d(S)(& sdot;), d(I) (& sdot;), q(S) and q(I) , and involving single limits and double limits. Finally, some open questions are proposed for the model, left us to further explore. Compared with the existing results for the constant diffusion rates and common advection rate, our model is more general and more complicated, the results established in this paper are richer and more meaningful

In this paper, a two-patch epidemic model incorporating migration-mediated multi-threshold control strategies is proposed to explore the effect of migration and adaptive interventions (e.g, lockdown) on disease transmission. If the numbers of infected individuals in both patches are below a predefined threshold (I1 < Ic, I2 < Ic), migration between patches could occur freely; if Ii>Ic(i=1or2), the ith patch would be put under surveillance with a partial lockdown, only essential personnels (e.g., healthcare workers) could migrate between patches at saturated rates; if I1 > Ic, I2 > Ic, a complete lockdown would be imposed on both patches. The global dynamics of proposed Filippov system is analysed, including the existence and stability of disease-free, boundary, and endemic equilibria. Especially, the sliding mode dynamics on switching surfaces, i.e., multiple pseudo-equilibria and bifurcations (e.g., saddle-node, Hopf, Bogdanov-Takens and period-halving) are discussed in detail, which could exactly characterize the critical tipping points in epidemic transmission trajectories. Numerical simulations demonstrate that if some appropriate thresholds on migration regulation between two patches are chosen, the number of infected individuals can be effectively controlled at a desired low level, which could further potentially curb the disease spread.

In this paper, a SIRP epidemic model is proposed, wherein the pathogens derive from two ways, i.e., environmental breeding, and accumulative excretion by the infected individuals. The former is characterized by Logistic growth, while the latter is in the form of infinite integral. First, the positivity and ultimate boundedness of solutions are obtained. Second, the basic reproduction number R0 is obtained, by which the model is analyzed if either the intrinsic growth rate of environmental pathogens is lower or higher than its clearance rate. For the first case, the disease-free equilibrium is globally asymptotically stable when R0 < 1, while the endemic equilibrium is globally asymptotically stable when R0 > 1. Conversely, if the growth rate exceeds the removal rate, the disease-free equilibrium is always unstable, meanwhile, the uniform persistence of the model indicates that there could exist one or multi-endemic equilibria, and it is globally asymptotically stable if the endemic equilibrium is unique. Finally, the theoretical results are illustrated by numerical simulations. We find that the accumulative release of pathogens by the infected individuals in the form of infinite integral is more realistic and consistent with the disease spread than that of linear form by real data.

In this paper, a SVEIRDP epidemic model is proposed to investigate the transmission dynamics of Ebola by cumulative release from the infected individuals and corpses in the form of infinite integrals. First, the positivity and ultimate boundedness of solutions are proved. Second, the basic reproduction number R0 is calculated. Furthermore, it is proven that if R0<1, the model has the disease-free equilibrium and is globally asymptotically stable (GAS); If R0>1, the unique endemic equilibrium is GAS. To clearly illustrate the theoretical results, real data are used to conduct numerical simulations. We discover that modeling the cumulative release of Ebola from the infected individuals and corpses using the infinite integral with an appropriate probability density function (PDF) provides a more realistic and accurate representation of the actual disease spread.

To research the combined impacts of mean-reverting white noise and spatial diffusion on the transmission of Kawasaki disease (KD), this paper introduces a stochastic reaction-diffusion model for KD incorporating the Ornstein-Uhlenbeck (O-U) process. Firstly, for the deterministic reaction-diffusion model, the local and global stability of the inflammatory factors-free equilibrium (IFFE) and inflammatory factors-existent equilibrium (IFEE) based on basic reproduction number R_0 are discussed: when R_0<1 , the IFFE is globally asymptotically stable and the IFEE is globally asymptotically stable when R_0>1 and certain additional conditions are satisfied. Then, for the stochastic reaction-diffusion model, the existence of a unique solution is proven by constructing a Lyapunov function. Additionally, adequate conditions for the existence of the unique stationary distribution for the positive solution are provided. Finally, numerical simulations are conducted to explore the effects of noise intensity and spatial diffusion on KD, the results show that when the noise intensity is fixed in a certain interval and the diffusion coefficient is greater than a certain value, the disease is persistent. In addition, when the noise intensity is equal to zero, the dynamic behaviors of the stochastic reaction-diffusion system are consistent with the deterministic reaction-diffusion system.

In this paper, a within-body co-infection model is proposed to characterize the dynamics of interactive spread between HIV and Mycobacterium tuberculosis. The locally and globally asymptotic stabilities of disease-free and endemic equilibria on both two single infection systems, i.e., only HIV or Mtb infection model are derived based on the basic reproduction number R-V,R-B, respectively. The basic reproduction number R-VB of the co-infection model is acquired, and the locally and globally asymptotic stability of disease-free equilibrium are obtained when R-VB<1, while if R-VB>1 and the invasion reproduction numbers R-V(1)>1, R-B(1)>1, the uniform persistence of disease is also acquired, meanwhile there exists at least one co-infection endemic equilibrium. The theoretical results with numerical simulations are verified, revealing the magnitude and impact of co-infection is much larger than that of single infection, and the disease burden of host would greatly increase if the two kinds of pathogen act synergistically.

In this paper, a delayed multi-strain patch SIS epidemic model with varying incidence and migration of susceptible individuals induced by media coverage of infected individuals is proposed. For the subsystem without migration, if there is no delay, criteria on the globally asymptotical stability of (disease-free, dominant and coexistent) equilibria are obtained. Otherwise, criteria on the local Hopf bifurcations at the dominant and coexistent equilibria are obtained, meanwhile, the global Hopf bifurcation is unbounded. For the model with migration, the basic reproduction number R0 is derived, by which criteria on the locally and globally asymptotic stability of disease-free equilibrium are derived. The uniform persistence of (strain 1 or 2 dominant and coinfection) disease are obtained respectively. The theoretical results are illustrated by numerical simulation, from which we find that R0 is non-monotonic with the migration rates between patches. Ignoring the multi-strain factor will greatly underestimate the scale of the disease, and even obtain the opposite conclusion (disease extinction or persistence). Delay could cause periodic oscillation, and the multi-strain and migration between patches could further produce chaos. Both the media effect with delay and migration could greatly influence the transmission dynamics of disease from stability to unstability until chaos, which further increase the difficulty of disease control.

The continuous increase in flight speed of aircraft makes the thermal environment more severe. The thermal environment causes significant deviations between the actual performance and design performance of the structure. Considering the impact of thermal environment during the structural design phase is crucial for a refined design. This paper proposes a novel multi-scale topology optimization method for thermo-elastic structures considering performance reduction caused by temperature for the first time. Firstly, the variation law of the material properties affected by temperature is analyzed and quantified. Then, the influence mechanism of temperature on the mechanical response of multi-scale structures is analyzed, including thermal load and performance reduction. The implementation process of the proposed method is introduced and validated through numerical examples, demonstrating the efficiency, effectiveness, and generalization ability of the method. The influence characteristics of temperature gradient and maximum temperature on multi-scale structures are analyzed through numerical examples. Research work can provide important references for improving the physical properties of advanced materials.

Considering the effects of commercial heterosexual behavior and environmental noise on the dynamics of HIV/AIDS disease, in this study, we establish a stochastic HIV/AIDS model that combines commercial heterosexual behavior and ln-type Ornstein-Uhlenbeck process. Firstly, for the deterministic model, i.e., the stochastic noise is not taken into account, the local and global asymptotic stability of the equilibria in terms of basic reproduction number R-0 are given. Then, for the stochastic model, the uniqueness and existence of global solutions, the existence of stationary distribution under R-0(S)>1, and the exponential extinction of HIV-positive patients under R-0(E)<1 can all be obtained by constructing suitable random Lyapunov functions. In particular, under certain conditions, specific expression of the probability density function near the quasi-endemic equilibrium of the stochastic system can be obtained. Finally, numerical simulations indicate that controlling noise intensity, as well as commercial heterosexual activities, can help control the transmission of HIV.

In this paper, a class of hematopoietic stem cell transplantation model with virus-to-cell HIV infection and ratio-dependent recruitment is proposed to characterize the competitive exclusion and coexistence between the host CD4+T cells and donor CD4+T cells. First, the positivity and boundedness of solutions as well as the basic reproduction number are obtained. Second, criteria on the locally and globally asymptotical stability of all feasible equilibria are established. Furthermore, bifurcation analysis is performed on the mixed chimerism infection equilibrium. Finally, the theoretical results are illustrated by numerical simulation, we find that chimerism is an important indicator of model stability, and AIDS may be cured when chimerism reaches a certain threshold.

In this paper, a delayed double-strain influenza model with vaccination and cross-immunity is proposed to explore the effect of coinfection of double-strain on disease spread. First, the nonnegativity and ultimate boundedness of solution are proved. Second, the basic reproduction numbers of strains 1, 2, and the whole model are defined respectively, by which criteria on the local and global asymptotic stability of (disease-free, dominant) equilibria are established. The uniform persistence of (strains 1, 2 coexistent) disease is obtained as well. Finally, the validity of the theoretical results is demonstrated by numerical simulations. We find that neglecting cross-immunity and vaccination would misestimate the size of influenza outbreaks. Cross-type multivalent vaccines will be the main direction for effective control measure for influenza.

In this paper, a coupling cholera epidemic model is proposed, in which the pathogens could both spread within-host and between-host, meanwhile, there exist age-dependent infection between the asymptomatic and symptomatic infected people. For the fast-time subsystem, the infection-free and endemic equilibria are both globally asymptotically stable. For the slow-time subsystem, the basic reproduction number R0 is determined, by which we observe that the disease-free equilibrium is globally asymptotically stable (the absence of pathogens in environment) if R0<1, while the endemic equilibrium is globally asymptotically stable (the presence of pathogens in environment) when R0>1. The theoretical results are illustrated by numerical simulations, by which we find that age-dependent and asymptomatic infections may further promote cholera spread. Besides, the linking of pathogen transmission at the individual level with infection at the population level could result in forward or backward bifurcation.