Mathematical analysis and stability switching in a delayed disease transmission model

In this paper, we propose a mathematical model to describe the transmission dynamics of infectious diseases with targeted antiviral prophylaxis strategy. Our model incorporates seasonal driving force since seasonal force has a great effect on the spread of infectious diseases. Based on the local stability of disease free equilibrium we derive the control reproduction number [Formula: see text]. Sufficient conditions for the global stability of the disease free equilibrium are obtained. Using the persistence theory for discrete dynamical system, we prove that the infectious disease will remain endemic if [Formula: see text]. Simulation results are also provided to study the effect of targeted antiviral prophylaxis on transmission dynamics of infectious disease and investigate the influence of seasonality on the efficiency of targeted antiviral prophylaxis strategy.

We introduce and analyze an infectious disease model that combines the Crowley–Martin incidence rate with the Holling-type II treatment rate. This model aims to capture the transmission dynamics of infectious diseases and takes into account the potential for reinfections. We thoroughly examine the behavior and characteristics of this model to gain insights into the spread and control of infectious diseases. We obtained the case of transcritical and backward bifurcations conditionally. The global stability of a unique endemic steady state is obtained under appropriate parametric conditions, as demonstrated using a geometric approach. When the basic reproduction number exceeds one, the system exhibits the coexistence of numerous endemic steady states. These steady states give birth to complex and sophisticated dynamics because they display a variety of bifurcations, oscillations (via Hopf bifurcation), bistability, and hysteresis. Through the use of sensitivity analysis, the parameters that are most sensitive to the basic reproduction number are identified. The theoretical results are accompanied by their corresponding numerical simulations. This work highlights the importance of ensuring proper access to effective treatment and preventing reinfection to achieve the ultimate goal of disease eradication.

This study presents a nonlinear SEIR Stype epidemic model with media impact for transmission dynamics of infectious diseases which leads to many behavioral and societal changes related to with the synchronous spread of awareness among masses. We analyzed the model with endemic equilibrium points with basic reproduction which is used to explore the permanency of the solid conditions. Dynamical behavior of mathematical model around biologically possible region provides statistics around the range of infective viruses among population. Mathematical analysis of forward and backward bifurcation is also obtained. The optimality of the media coverage is also presented. Numerical results are performed to explore the effect of media on different dynamical regions.

Wheat is one of the most significant crops grown worldwide and serves as both an important source of food for consumers and a means of income for farmers. However, the fungus that causes wheat yellow rust (WYR) seriously damages the world’s wheat production, especially in developing countries. In this study, we proposed and analyzed a compartmental mathematical model to describe the transmission dynamics of WYR disease on wheat crops. For the proposed model, the existence and uniqueness, the positivity and boundedness of the solutions are explained. The two equilibrium points, namely disease-free and endemic equilibrium points are demonstrated, and the basic reproduction number is evaluated using the next-generation matrix approach. The Routh Hurwitz stability criteria and center manifold theory are used to analyze the local stability of the equilibrium points and the existence of forward bifurcation, respectively. The global stability of the equilibrium points are also established using Lyapunov’s approach. A sensitivity analysis of the model is also carried out. To validate our analytical results, MATLAB software is utilized to conduct several numerical simulations and generate graphical representations of the results. The findings of this study suggest that effective use of fungicides can significantly prevent the spread of WYR disease.

SIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure may be incorporated. Previous analyses assumed identical waning rates from R to W and from W to S. This implicitly assumes equal length for the period of full immunity and of waned immunity. We relax this restriction, and allow an asymmetric partitioning of the total immune period. Stability switches of the endemic equilibrium are investigated with a combination of analytic and numerical tools. Then, continuation methods are applied to track bifurcations along the equilibrium branch. We find rich dynamics: Hopf bifurcations, endemic double bubbles, and regions of bistability. Our results highlight that the length of the period in which waning immunity can be boosted is a crucial parameter significantly influencing long term epidemiological dynamics.

Optimal control and the value of information for a stochastic epidemiological SIS-model

Modelling and predicting the behaviour of infectious diseases is essential for early warning and evaluating the most effective interventions to prevent significant harm. Compartmental models produce a system of ordinary differential equations (ODEs) that are renowned for simulating the transmission dynamics of infectious diseases. However, the parameters in compartmental models are often unknown, and they can even change over time in the real world, making them difficult to determine. This study proposes an advanced artificial intelligence approach based on physics-informed neural networks (PINNs) to estimate time-varying parameters from given data for the compartmental model. Our proposed PINNs method captures the complex dynamics of COVID-19 by integrating a modified Susceptible-Exposed-Infectious-Recovered-Death (SEIRD) compartmental model with deep neural networks. Specifically, we modelled the system of ODEs as one network and the time-varying parameters as another network to address significant unknown parameters and limited data. Such structure of the PINNs method is in line with the prior epidemiological correlations and comprises the mismatch between available data and network output and the residual of ODEs. The experimental findings on real-world reported data data have demonstrated that our method robustly and accurately learns the dynamics and forecasts future states. Moreover, as more data becomes available, our proposed PINNs method can be successfully extended to other regions and infectious diseases.

The spread of infectious diseases has always been of concerns and a threat to public health. It has caused serious problems for the survival of human beings and other species. In epidemiology, mathematical models are the basic conceptual tools used to understand epidemic dynamics and to formulate control strategies. A mathematical model of the transmission dynamics of infectious disease is an important theoretical epidemiology method, which has been used to simulate in analyzing and control of infectious diseases. In this paper, we will discuss about disease model with infection-stage structure, where the period of infection is partitioned into two stages: the acute and the chronic stages. The disease-free equilibrium was locally asymptotically stable when R 0 < 1 and the endemic equilibrium was locally asymptotically stable when R 0 > 1.

The kernel of modelling transmission dynamics of infectious diseases lies in constructing the force of infection (FOI). Traditionally, it was based on mass-action law. In this paper, we show, based on survey data of Escherichia coli O157 infection on Scottish cattle farms, that the actual form of FOI deviates greatly from mass-action law. Further, control effectiveness deviates qualitatively: the epidemic of mass-action FOI can be controlled with a control effort larger than the so-called herd immunity, while the epidemic inferred from the survey data of E. coli O157 infection was shown to be difficult to control. This indicates that, at least for E. coli O157 infection on cattle farms, it is risky to rely on models of transmission dynamics that were based on mass-action law to design the optimal intervention programme for infectious diseases. This suggests the importance of collecting epidemic data and model selection from data-driven models to infer the most likely model of transmission dynamics.

The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.

This study examines the spatiotemporal dynamics of Bacillus anthracis, the causative agent of anthrax, under climate change scenarios using advanced machine learning techniques. Climate change is increasingly recognized as a critical factor influencing the distribution and transmission dynamics of infectious diseases, particularly those reliant on environmental reservoirs. Our research employs Maximum Entropy (Maxent) modeling to forecast the current global distribution of B. anthracis based on climatic factors and to predict future habitat suitability under various Coupled Model Intercomparison Project Phase 5 (CMIP5) scenarios (RCP-2.6 and RCP-8.5) for the 2050’s and 2070’s. We identify high-risk areas where climate change may enhance the suitability for B. anthracis, emphasizing the need for proactive monitoring and early-warning systems. The findings indicate potential shifts in anthrax-endemic zones, with new regions becoming conducive to the establishment of B. anthracis due to the changing climate. Our results demonstrate the applicability of machine learning in predicting disease risk, providing a framework for public health preparedness in light of evolving environmental challenges. These insights are critical for developing targeted surveillance strategies and mitigating the introduction of zoonotic diseases in a warming environment.

Toxoplasmosis, caused by the intracellular parasite Toxoplasma gondii, affects a wide range of warm-blooded animals, including humans. Domestic and wild felines serve as definitive hosts, excreting oocysts that contaminate the environment. Intermediate hosts, such as the endangered European mink (Mustela lutreola) and the non-native American mink (Neogale vison), can become infected primarily through the ingestion of tissue cysts present in prey, while the ingestion of oocysts from contaminated soil or water plays a secondary role. This study analyzed the seroprevalence of T. gondii in 179 mink specimens (137 American mink and 42 European mink) collected in northern Spain from 2014 to 2020. Using an optimized indirect immunofluorescence assay, antibodies against T. gondii were detected in 47 samples (37 American mink and 10 European mink). Seroprevalence was higher in the Ebro basin than in the Cantabrian region, although the difference was not statistically significant. No significant associations were observed between seropositivity and species, sex, or habitat. These findings suggest environmental contamination by T. gondii oocysts in northern Spain and underscore the potential value of invasive American mink as sentinel species for monitoring public health risks associated with this parasite. The study also highlights the importance of wildlife surveillance in assessing environmental contamination and understanding transmission dynamics of infectious diseases in ecosystems.

Mathematical models of transmission dynamics of infectious diseases provide a useful tool for investigating the impact of community based control measures. Previously, we used a dynamic (constant force-of-infection) model for lymphatic filariasis to describe observed patterns of infection and disease in endemic communities. In this paper, we expand the model to examine the effects of control options against filariasis by incorporating the impact of age structure of the human community and by addressing explicitly the dynamics of parasite transmission from and to the vector population. This model is tested using data for Wuchereria bancrofti transmitted by Culex quinquefasciatus in Pondicherry, South India. The results show that chemotherapy has a larger short-term impact than vector control but that the effects of vector control can last beyond the treatment period. In addition we compare rates of recrudescence for drugs with different macrofilaricidal effects.

ABSTRACTStochastic delayed modeling (stochastic differential equations [SDEs] with delay parameters) has a significant nonpharmaceutical intervention to control transmission dynamics of infectious diseases, and its results are close to the reality of nature. According to the report of the World Health Organization (WHO), 296 million people are infected, and approximately 1.5 million people report positive tests for Hepatitis B each year. Hepatitis B is still a threat in developing and developed countries and appears in different variants globally. The present study is an extension of the deterministic hepatitis B model into a stochastic delayed model. The incorporation of stochasticity with delay in each compartment of the population like the S(t) susceptible population, P(t) acute infection, Q(t) chronic carriers' cases, R(t) immunization cases, and H(t) vaccinated class. The essential properties like positivity, boundedness, existence, uniqueness, equilibria (hepatitis‐free equilibrium [HFE] and hepatitis‐existing equilibrium [HEE]), reproduction number, sensitivity analysis, and stability result in the sense of local and second‐order stability result in the sense of global are studied rigorously before an extension of the model. The nonparametric perturbation and transition probabilities ways used to extend analysis. Also, the positivity, boundedness, extinction, and persistence of disease are studied rigorously. Due to the high complexity of nonlinear stochastic delay differential equations, computational methods are used to visualize the results with data from the model. Unfortunately, the existing methods (Euler–Maruyama, stochastic Euler, and stochastic Runge–Kutta) in the literature fail to restore the dynamical properties of the model and make a comparison with the newly proposed construction of nonstandard finite difference method in the sense of stochastic. In the proposed method, all dynamic properties of the model are restored with a free choice of time steps, and it is efficient. For convenience, a computational code of the nonstandard discrete model may be provided to the readers at their request.

Experimental investigation and design method for the shear strength of self-piercing rivet connections in thin-walled steel structures