Mathematical Biosciences and Engineering最新文献

We consider a two-Patch malaria model, where the individuals can freely move between the patches. We assume that one site has better resources to fight the disease, such as screening facilities and the availability of transmission-blocking drugs (TBDs) that offer full, though waning, immunity and non-infectivity. Moreover, individuals moving to this site are screened at the entry points, and the authorities can either refuse entry to infected individuals or allow them in but immediately administer a TBD. However, an illegal entry into this Patch is also possible. We provide a qualitative analysis of the model, focusing on the emergence of endemic equilibria and the occurrence of backward bifurcations. Furthermore, we comprehensively analyse the model with low migration rates using recent refinements of the regular perturbation theory. We conclude the paper with numerical simulations that show, in particular, that malaria can be better controlled by allowing the entry of detected cases and treating them in the better-resourced site rather than deporting the identified infectives and risking them entering the site illegally.

Hes1 (Hairy and enhancer of split 1) is a transcriptional repressor that plays a fundamental role in the regulation of embryogenesis and cell lineage specification. The temporal dynamics of Hes1 mRNA and Hes1 protein expression are known to exhibit sustained oscillations. However, many existing mathematical models can reproduce these oscillations only transiently, eventually dampening toward a steady state. This limits their biological fidelity, as sustained oscillations are observed in vitro and in vivo under physiological conditions. To address these limitations, we propose a more biologically realistic framework by incorporating both transcriptional/translational time delays and spatial diffusion effects into a Reaction-Diffusion (RD) system with discrete time delays. The model describes the spatiotemporal dynamics of Hes1 mRNA and protein concentrations in the cytoplasm and nucleus. We establish the conditions under which the RD model undergoes a delay-induced Hopf bifurcation, leading to the emergence of stable periodic solutions. Furthermore, our analysis establishes explicit criteria on the delay and diffusion coefficients that ensure the existence of sustained oscillatory patterns. Numerical simulations are conducted to validate the theoretical predictions, demonstrating the persistence and stability of oscillations under a range of biologically plausible parameters.

Ecosystem stability is increasingly threatened by rapid environmental fluctuations that alter species interactions and survival strategies. Traditional steady-state analyses often overlook transient dynamics that govern ecosystem responses to accelerating change. This study explored rate-induced tipping (R-tipping), a phenomenon where environmental change rates outpace species' adaptive capacity, triggering abrupt shifts between ecological states. Our findings demonstrate that species persistence depends on a delicate balance between cooperation-associated costs, population densities, and environmental variation rates. Under moderate fluctuations, species can track unstable states before reaching new equilibria, enhancing resilience. However, beyond critical thresholds, homoclinic and saddle-node bifurcations destabilize coexistence induced with increasing cooperation strength, leading to extinction cascades. By integrating time-dependent basin stability analysis, we uncovered mechanisms driving ecological transitions and identified key factors influencing long-term persistence. This research highlights the need for dynamic models to predict tipping events and informs conservation strategies for mitigating biodiversity loss in rapidly changing environments.

The most widely used measurement of transmission dynamics in real time is the effective reproduction number $ Rleft(tright) $. However, in the context of human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS), $ Rleft(tright) $ has not been used frequently, possibly because of the slowly progressing nature of HIV infection that limits the knowledge of recent infection events. Gaining deeper insights into the practically used epidemiological metrics of HIV/AIDS is therefore vital. Notably, in many high-income countries, including Japan, the rate of clinical AIDS on diagnosis, $ Qleft(tright) $, has been routinely measured by calculating the proportion of newly diagnosed AIDS cases out of all new HIV infections that are diagnosed at a given calendar time. However, there has been no clear indication of whether the control of HIV/AIDS is effective in relation to this metric in Japan. In this study, we formulated the rate of clinical AIDS on diagnosis using a mathematical model and offered interpretations of it using the hazard rate of diagnosis among previously undiagnosed HIV-infected individuals. We showed that by taking the inverse of the odds of $ Qleft(tright) $ and multiplying it by the inverse of the mean incubation period, we obtained $ alpha left(tright) $, which is the hazard rate of diagnosis among undiagnosed HIV-infected individuals. We also showed that $ alpha left(tright) $ can be related to the goal of the diagnosed proportion $ {P}_{0} $ among all people living with HIV. In addition to the rate of clinical AIDS on diagnosis $ Qleft(tright) $, $ alpha left(tright) $ can be calculated using a simplistic equation and can potentially act as a practical epidemiological metric for monitoring during surveillance.

Malaria is a life-threatening mosquito-borne infectious disease prevalent in tropical regions, primarily transmitted to humans by the bites of infected Anopheles mosquitoes. This study presents a mathematical model analysis aimed at understanding the dynamics of malaria transmission and the effectiveness of various prevention strategies. Despite being preventable and curable, malaria continues to pose significant public health challenges, notably due to the risk of recurrent infections if improperly treated. The proposed deterministic model establishes the positivity and boundedness of solutions alongside the local stability of equilibria. A sensitivity analysis is conducted to identify key parameters impacting the basic reproduction number ($ R_0 $), which is crucial for evaluating intervention strategies. The findings indicate that although the current vaccines are not $ 100% $ effective, vaccination could significantly contribute to malaria control alongside existing preventive measures, such as mosquito nets and insecticide spraying. The study underscores the need for a comprehensive approach combining multiple strategies to effectively reduce malaria transmission and improve health outcomes in endemic regions. Overall, this research highlights the importance of mathematical modeling in formulating effective disease control policies.

The hydrologic cycle is increasingly disrupted due to the rising human population and the associated decline in forest trees. The rationale of this work was to address the disruption in the hydrologic cycle, which is caused by the dual adverse effects of human population growth: reducing forestry trees and diminishing clouds' formation. The proposed model assumes that the density of forestry trees decreases due to harvesting activities to fulfill the resource demands of human population. Additionally, it posits that the transpiration from forestry trees contributes to an increased density of vapor clouds' formation, while population growth adversely impacts the natural formation rate of vapor clouds. The model was analyzed by employing qualitative analysis, demonstrating the feasibility and stability of equilibrium solutions. Furthermore, to capture the consequences of environmental fluctuations on the model's dynamics, the proposed deterministic model was extended to a stochastic framework. The analytical and numerical work sought to provide the directives for understanding and mitigating the adverse effects of human activities on the hydrologic cycle, promoting sustainable practices to restore ecological equilibrium. Results of the model analysis reveal that an increase in human population leads to a decline in both rainfall and forestry trees. However, reforestation with high-transpiration tree species can mitigate rainfall decline and restore balance to the hydrologic cycle. Moreover, the maximum density of forest trees is achieved when the utility of rain by the forest trees and the natural formation of vapor clouds are maximal. Also, the minimal anthropogenic hindrance in reducing the natural formation of vapor clouds, combined with the maximal efficiency of vapor clouds to naturally convert into raindrops, facilitates maximum rainfall.

Historically, the world has endured numerous respiratory pandemics, with the recent COVID-19 outbreak underscoring the significant importance of respiratory equipment and mechanical ventilators being no exception. Despite long-standing efforts in control and modeling system research, mechanical ventilators, especially the air generation unit, remain a significant challenge due to various factors and uncertainties (e.g., model structure, order selection, time-varying parameters, etc.). This paper presents a novel approach for identifying ARMA models, specifically in ventilation pumps, using Ridge regression modified with momentum (Ridge-M) and a grid search-based joint optimization strategy. The proposed algorithm effectively estimates model coefficients while simultaneously selecting the optimal AR and MA orders along with time-delay parameters. By integrating momentum into Ridge regression, the estimation process gains stability and improved convergence, particularly in handling abrupt system changes. The grid search framework ensures robust model selection by systematically evaluating candidate structures using the Akaike Information Criterion (AIC). Experimental validation with multiple input functions, including ramp and multistep signals, demonstrates that Ridge-M achieves superior performance in capturing dynamic system behaviors. Ridge-M reduces the root mean squared error (RMSE) by 2.7% on average across multistep inputs for both scenarios compared to recursive least squares and 6.8% compared to standard Ridge regression. However, standard Ridge outperforms Ridge-M for ramp inputs for both scenarios, reducing RMSE by 0.7%, indicating that momentum can slow adaptation to gradual variations. Nonetheless, Ridge-M achieves the lowest overall average RMSE (31.6236) compared to RLS (34.1499) and standard Ridge regression (32.0247), confirming its superior balance between stability and adaptability in model identification. This work offers a lightweight and stable method that is well-suited for embedded applications where data is noisy, the system is time-varying, and computational resources are limited.

We consider the Gause predator-prey with general bounded or sub‑linear functional responses, - which includes those of Holling types Ⅰ-Ⅳ. - and multiplicative Gaussian noise. In contrast to previous studies, the prey in our model follows logistic dynamics while the predator's population is solely regulated by consumption of the prey. To ensure well-posedeness, we derive explicit Lyapunov-type criteria ensuring global positivity and moment boundedness of solutions. We find conditions for noise‑induced extinctions, proving that stochasticity can drive either population to collapse even when the deterministic analogue predicts stable coexistence. In the case when the predator becomes extinct, we establish a limiting distribution for the predator's population. Last, for functional responses of Holling type Ⅰ, we provide sufficient conditions on the intensity of the noise for the existence and uniqueness of a stationary distribution.

The cannibalistic behavior of Tribolium has been extensively researched, revealing instances of chaotic dynamics in laboratory environments for Tribolium castaneum. The well-established Larvae-Pupae-Adult (LPA) model has been instrumental in understanding the conditions that lead to chaos in flour beetles (genus: Tribolium). In response to new experimental observations showing a decline in the pupae population in Tribolium confusum, we proposed and analyzed a simplified two-stage Larvae-Adult (LA) model. This model integrated the pupae population within the larval group, similar to that of the original LPA model, with development transitions governed by internal rates. By applying the model to time-series data, we demonstrated its effectiveness in capturing short-term population fluctuations in T. confusum. We established the model's positivity and boundedness, perform stability analyses of both trivial and positive steady states, and explored bifurcations and steady-state behavior through numerical simulations. We proved global stability for the extinction and positive steady states and observed additional restrictions required for stability compared to the LPA model. Our results indicated that while chaos was a possible outcome, it was infrequent within the practical parameter ranges observed, with environmental changes related to media and nutrient alterations being more likely triggers.

Zika virus is spread to human populations primarily by Aedes aegypti mosquitoes, and Zika virus disease has been linked to a number of developmental abnormalities and miscarriages, generally coinciding with infection during early pregnancy. In this paper, we propose a new mathematical model for the transmission of Zika and study a range of control strategies to reduce the incidence of affected pregnancies in an outbreak. While most infectious disease models primarily focus on measures of the spread of the disease, our model is formulated to estimate the number of affected pregnancies throughout the simulated outbreak. Thus the effectiveness of control measures and parameter sensitivity analysis is done with respect to this metric. In addition to traditional intervention strategies, we consider the introduction of Wolbachia-infected mosquitoes into the native population. Our results suggest a threshold parameter for Wolbachia as an effective control measure, and show the natural time scale needed for Wolbachia-infected mosquitoes to effectively replace the native population. Additionally, we consider the possibility of a Zika vaccine, both to avoid an outbreak through herd immunity and as a control measure administered during an active outbreak. With emerging data on persistence of Zika virus in semen, the proposed compartmental model also includes a component of post-infectious males, which introduces a longer time scale for sexual transmission than the primary route. While the overall role of sexual transmission of Zika in an outbreak scenario is small compared with the dominant human-vector route, this model predicts conditions under which subpopulations may make this secondary route more significant.