This paper deals with a diffusive Leslie–Gower model with a strong Allee effect on the prey and a fear effect on the predator. We first consider the stability of positive constant solutions of the system in the absence of diffusion. Furthermore, we analyze the Turing instability phenomenon in positive constant solutions resulting from diffusion effects. Moreover, we investigate steady-state bifurcations using the Lyapunov–Schmidt reduction. The research establishes that diffusion can induce instability in these solutions. To validate these findings, we present numerical simulations, suggesting the model's potential to generate spatial patterns under specific conditions.
Hospitalized patients are particularly susceptible to infections brought on by methicillin-resistant Staphylococcus aureus (MRSA), and these infections usually have a high morbidity and mortality rate. Several strategies can help prevent MRSA from spreading, but the efficacy of each strategy remains unclear, as most past research evaluated multiple interventions together rather than examining each one individually. To assess the effects of hand hygiene and screening, we created a novel compartmental MRSA spread framework for healthcare facilities in Edmonton, Alberta. The model accounts for MRSA patients (hospital-acquired (HA) MRSA or community-acquired (CA) MRSA colonization or infections) and isolated patients. To examine the effects of interventions, we first estimated the posterior mean of the parameters in our model, as well as a sub-model of it, using a Bayesian framework with Markov chain Monte Carlo (MCMC) techniques, utilizing data from hospitals in Edmonton. Next, we incorporated different intervention rates into the model to ascertain their effect on colonized and infected patients. One intervention is practicing hand hygiene among healthcare workers in hospitals to reduce transmission rates between susceptible individuals and MRSA patients. The other intervention is to screen patients for MRSA colonization to place them in isolation rooms swiftly. The two interventions were first examined alone, and then simultaneously. We compared the overall number of HA-MRSA colonization and infections as the intervention rates varied, and the findings show that combined interventions are more effective than individual interventions at limiting MRSA transmission in hospitals.
Human papillomavirus (HPV) remains one of the most common sexually transmitted infections worldwide, and its persistence and possible reactivation complicate efforts to understand and control transmission. In particular, the presence of a carrier stage and variation in reactivation across age and sex may play important roles in maintaining HPV prevalence. In this paper, we develop a two-sex Susceptible-Infectious-Carrying-Recovered (SICR) model with n discrete age groups to investigate how age-specific and sex-specific reactivation rates affect HPV transmission dynamics and how control measures can be designed accordingly. We derive the basic reproduction number R0 and show that it provides a threshold criterion for disease elimination. The existence and stability of both the disease-free equilibrium and the endemic equilibrium are established rigorously. Using epidemiological data from Hangzhou in 2011, we estimate R0 to be 2.177. Analytical and numerical results show that viral reactivation plays an important role in sustaining HPV endemicity and highlight the need for age-specific and sex-specific public health strategies. We also find that an excessively low viral reactivation rate is not always beneficial for controlling HPV prevalence. In particular, regulating reactivation alone is insufficient to control HPV transmission effectively, and our results suggest that combined interventions targeting both transmission and reactivation are more effective.
Tuberculosis (TB) remains a major public health burden in Kyrgyzstan; however, the seasonal transmission dynamics of TB in the country have not been quantitatively characterized. This study aimed to develop a seasonal dynamic model to simulate TB transmission, estimate the basic reproduction number R0, assess transmission intensity, and inform evidence–based prevention and control strategies. Using monthly reported new TB cases from the national TB surveillance and registration system in Kyrgyzstan from 2022 to 2025, we constructed a seasonal SEIR model incorporating periodic transmission and reactivation rates. Model parameters were estimated using a Bayesian Markov chain Monte Carlo (MCMC) method. R0 was calculated using two methods: the periodic time–varying method and the annual average transmission rate method. Local sensitivity analysis was performed to evaluate the impact of the baseline transmission parameter as and the baseline reactivation parameter ae on TB transmission dynamics. The model adequately captured the seasonal fluctuations and overall downward trend in new TB cases, achieving a mean absolute percentage error (MAPE) of 8.66% and a root mean square percentage error (RMSPE) of 9.95%. The estimated periodic R0 was 0.8842 (95% credible interval [CrI]: 0.8811–0.8873), which remained below the threshold of unity. Assuming no change in current prevention and control measures, projections suggest a gradual decline in monthly new TB cases, with the annual number of new cases declining to approximately 2902 by 2126. These results indicate that TB transmission has not been fully interrupted and that elimination is unlikely to be achieved within the projection period. Sensitivity analysis revealed that both as and ae substantially affected the number of new TB cases and R0, and that modest changes in these parameters could drive R0 above the threshold of unity. The seasonal SEIR model provided a good fit to the monthly number of new TB cases in Kyrgyzstan. Although the estimated R0 is below the threshold of unity, indicating a declining epidemic trend, the rate of decline remains relatively slow, highlighting the need to sustain and strengthen prevention and control measures.
The dissemination of epidemic-related information can effectively enhance public awareness of preventive measures and decrease infection risks. However, information dissemination through multiple channels, including both online and offline sources, and the dynamics of information dissemination across these channels are influenced by individual mobility. To address this gap, this study develops a three-layer metapopulation network coupled model that integrates online information dissemination, epidemic spreading, and offline information dissemination. The proposed model systematically investigates the patterns of information dissemination through both online and offline channels, as well as the epidemic reaction–diffusion process driven by individual migration. Furthermore, the social interactions dynamics of both information channels are influenced by migration, manifested as migrated individuals acquire offline information in destination patches and establish online connections with individuals residing there. Theoretical analysis using the Microscopic Markov Chain Approach (MMCA) derives epidemic thresholds, while Monte Carlo (MC) simulations validate the model and examine factors influencing propagation dynamics. Results indicate that migration enhances individuals’ offline information acquisition, and accelerates cross-patch online information dissemination. Both online and offline information interactions exert inhibitory effects on epidemic spread, effectively increasing the infection threshold and reducing the outbreak scale. Furthermore, increasing the connectivity and dissemination rate of online information, particularly the information dissemination via weak relationships between patches, can effectively inhibit epidemic outbreaks. Notably, when the suppression effect of information on the epidemic is weak, population migration facilitates epidemic spread. In contrast, when the suppression effect is strong, migration-driven information dissemination significantly reduces the probability of infection, thereby further suppressing the outbreak.
