Search Results (75)

In this paper, we establish an age-structured SEIAR epidemic model that incorporates media effects and employ the exponential function approach to demonstrate the crucial role of media influence in disease prevention and control. Notably, our model accounts for the possibility of recessive infected individuals becoming dominant through contact with infectious individuals. Theoretical analysis yields the explicit expression for the basic reproduction number $R_0$, which serves as a critical threshold for disease dynamics. Through comprehensive threshold analysis, we investigate the existence and stability of both disease-free and endemic equilibrium states. By applying characteristic equation analysis and the method of characteristics, we establish the following: (1) when $R_0<1$, the disease-free equilibrium is globally asymptotically stable; (2) when $R_0>1$, a unique endemic equilibrium exists and maintains local asymptotic stability under specific conditions. This study shows that strengthening media promotion, raising awareness, and reducing the density of recessive infected individuals can effectively control the further spread of a disease. To validate our theoretical results, we present numerical simulations that quantitatively assess the impact of varying media reporting intensities on epidemic containment measures. These simulations provide practical insights for public health intervention strategies. Full article

This study establishes a fractional-order model (FOM) to describe the rumor spreading process. Members of society in this FOM are classified into three categories that change with time—the population that is ignorant of the rumors and does not know them, the population that is aware of the truth of the rumors but does not believe them, and the spreaders of rumors—taking into consideration awareness programs (APs) through media reports as a subcategory that changes over time where paying attention to these APs makes ignorant individuals avoid believing rumors and become better-informed individuals. We prove the positivity and boundedness of the FOM solutions. The feasible equilibrium points (EPs) and their local asymptotical stability (LAS) are analyzed based on the control reproduction number (CRN). Then, we examine the influence of model parameters that emerge with the CRN through a sensitivity analysis.A fractional optimal control problem (FOCP) is formulated by considering three time-dependent control measures in the suggested FOM to capture the spread of rumors; $u_1$, $u_2$, and $u_3$ represent the contact control between rumor spreaders and ignorant people, control media reports, and control rumor spreaders, respectively. We derive the necessary optimality conditions (NOCs) by applying Pontryagin’s maximum principle (PMP). Different optimal control strategies are proposed to reduce the negative effects of rumor spreading and achieve the maximum social benefit. Numerical simulation is implemented using a forward–backward sweep (FBS) approach based on the predictor–corrector method (PCM) to clarify the efficiency of the proposed strategies in order to decrease the number of rumor spreaders and increase the number of aware populations. Full article

Time delay and nonlinear incidence functions have a significant effect on rumor-spreading. In this article, a rumor-spreading model with two unequal time delays and a saturation effect is proposed. The existence, uniqueness, and non-negativity of the solution to this model are shown. The basic reproduction number is determined. A criterion for the existence of a rumor-endemic equilibrium is derived. It is found that there is an interesting conditional forward bifurcation. As a consequence, a complex bifurcation phenomenon is exhibited. A collection of criteria for the asymptotic stability of the rumor-free equilibrium are outlined. In the absence of a time delay, a criterion for the local asymptotic stability of the rumor-endemic equilibrium is presented. In the presence of small time delays, a criterion for the local asymptotic stability of the rumor-endemic equilibrium is established by applying our recently developed technique. Finally, a rumor-spreading control problem is reduced to an optimal control model, which is tackled in the framework of optimal control theory. This work facilitates the understanding of the influence of time delays and the saturation effect on rumor-spreading. Full article

This study develops a high-dimensional impulsive differential equation model to analyze Huanglongbing (HLB) transmission dynamics, incorporating seasonal fluctuations in vector psyllid populations and multi-pronged control measures: (1) periodic removal of infected/dead citrus trees to eliminate pathogen reservoirs and (2) non-uniform pesticide applications timed to disrupt psyllid life cycles. The model analytically derives the basic reproduction number ($R_0$) and proves the existence of a unique disease-free periodic solution. Theoretical analysis reveals a threshold-dependent stability: when $R_0<1$, the disease-free solution is globally asymptotically stable, ensuring pathogen extinction; when $R_0>1$, the system becomes uniformly persistent, indicating endemic HLB. Numerical simulations validate these findings and demonstrate that integrated interventions, combining psyllid population control and removal of infected plants, can significantly suppress HLB spread. The results provide a mathematical framework for optimizing intervention timing and intensity, offering actionable strategies for citrus growers. Full article

Understanding the effect of time delays on rumor spreading is of special importance to curbing the spread of rumors. This article proposes a rumor-spreading model with three identical time delays: a delay associated with the negative influence of a spreader on an exposed ignorant individual, a delay associated with the natural change from a spreader to a stifler, and a delay associated with the positive influence of a stifler on an exposed spreader. The basic reproduction number for the model is determined. A criterion for the existence of rumor-endemic equilibrium is provided. Interestingly, the model undergoes a conditional forward bifurcation. A collection of criteria for the asymptotic stability of the rumor-free equilibrium is derived. In the absence of a time delay, a criterion for the asymptotic stability of the rumor-endemic equilibrium is presented. By developing a novel technique for dealing with small time delays, a criterion for the asymptotic stability of the rumor-endemic equilibrium is established. Finally, the effect of some factors on the existence of rumor-endemic equilibrium is investigated. In particular, the effect of the time delay on rumor spreading is revealed. This work facilitates a deep understanding of the dynamics of rumor-spreading models with time delays. Full article

Diphtheria is a severely infectious and deadly bacterial disease with Corynebacterium diphtheriae as the causative agent. Since the COVID-19 pandemic, contagious diseases such as diphtheria have re-emerged due to disruptions in routine childhood immunization programs worldwide. Nigeria is witnessing a significant increase in diphtheria outbreaks likely due to an inadequate health care system and insufficient public enlightenment campaign. This paper presents a mathematical epidemic diphtheria model in Nigeria, which includes a public enlightenment campaign to assess its positive impact on the prevalence of the disease. The mathematical analysis of the model reveals two equilibrium points: the diphtheria infection-free equilibrium and the endemic equilibrium. These equilibrium points are shown to be stable globally asymptotically if ${\mathcal{R}}_c<1$ and ${\mathcal{R}}_c>1$, respectively. The model was fit using the confirmed diphtheria cases data of Kano State from January to December 2023. Sensitivity analysis indicates that the transmission rate and recovery rate of asymptomatic peopleare crucial parameters to be considered in developing effective strategies for diphtheria control and prevention. This analysis also reveals that the implementation of a high-level public enlightenment campaign and its high efficacy effectively reduce the prevalence of diphtheria. Finally, numerical simulations show that combining the public enlightenment campaign and isolating infected individuals is the best strategy to contain the spread of diphtheria. Full article

This paper proposes a multi-lingual S2IR rumor propagation model with white noise disturbances, aiming to study its dynamics and stochastic optimal control strategies. Firstly, a deterministic model is developed within a multi-lingual environment to identify rumor-free and rumor-spreading equilibria and calculate the basic reproduction number $R_0$. Secondly, a stochastic model incorporating white noise perturbation is developed, and the uniqueness of its global positive solution is examined. Meanwhile, the asymptotic behaviors of the model’s global solution near the steady states are discussed. Thirdly, the stochastic optimal control is designed to suppress the spread of rumors. Finally, the correctness and validity of the theoretical results are verified through numerical simulation. Full article

In this work, we propose and investigate a model of the dynamical behavior of HIV/AIDS transmission by considering a new compartment of the population with HIV: the latent asymptomatic class. The infection reproduction number that stabilizes the global dynamics of the model is evaluated. We analyze the model’s global asymptotic stability using the Lyapunov function and LaSalle’s invariance principle. To identify the primary factors affecting the dynamics of HIV/AIDS, a sensitivity analysis of the model parameters is conducted. We also examine a fractional-order HIV model using the Caputo fractional differential operator. Through qualitative analysis and applications, we determine the existence and uniqueness of the model’s solutions. We derive some results from the fixed-point theorem and Ulam–Hyers stability. Ultimately, the obtained numerical simulation results are in agreement with the analytical outcomes obtained from the model analysis. Our findings illustrate the efficacy of the fractional model in depicting the dynamics of the HIV/AIDS epidemic and offering critical insights for the formulation of effective control strategies. The results show that early intervention and treatment in the latent phase of infection can decrease the spread of the disease and its progression to AIDS, as well as increase the success of treatment strategies. Full article

A deterministic model for controlling the neglected tropical filariasis disease known as elephantiasis, caused by a filarial worm, is developed. The model incorporates drug resistance in human and insecticide-resistant vector populations. An investigation into whether the model is of biological importance reveals that it is positively invariant, mathematically well posed, and tractable for epidemiological studies. The filariasis-free and filariasis-present equilibrium points were obtained. The next-generation matrix technique is used to derive the basic reproduction number $R_0$, which is then used to determine the local stability analysis of the model. It is established that the system is locally asymptotically stable when $R_0<1$. The technique by Castillo-Chavez and a Lyapunov function were employed to prove the global stability of the model’s fixed points. The results of this analysis of filariasis-free equilibrium show that the system is globally asymptotically stable when $R_0<1$ and unstable when $R_0>1$. Similarly, the filariasis-present equilibrium point is proved to be globally asymptotically stable when $R_0>1$ and unstable otherwise. This indicates that the fight against the spread of the disease is achievable. It is observed that increasing human-infected mosquito contacts or mosquito-infected human contacts raises the value of $R_0$, whereas decreasing the progression of micro-filaria into infective larva and killing more mosquitoes will decrease the $R_0$ value according to the sensitivity analysis of the model. The variable precision arithmetic technique executed in MATLAB R2014a was used to determine the elasticity indices of the parameters of $R_0$, which showed that the value of $R_0=0.94639$. Further investigations revealed that ${\omega }_2$ has a significant influence on the reproduction number, suggesting that treatment of acute infections is crucial in the control of the disease. Pontryagin’s Maximum Principle (PMP) is used for optimal control analysis. The numerical result revealed that strategy D is the most effective based on the infection averted ratio (IAR) value. Full article

One of the main obstacles in rice cultivation is tungro disease, caused by Rice Tungro Spherical Virus (RTSV) and Rice Tungro Bacilliform Virus (RTBV), which are transmitted by green leafhopper vectors (Nephotettix virescens). This disease can be controlled by using pesticides and refugia plants. Excessive use of pesticides can have negative impacts and high costs, so it is necessary to control the use of pesticides. In this study, a mathematical model of the spread of tungro virus disease in rice plants was developed by considering the characteristics of the virus, the presence of green leafhoppers and natural enemies, refugia planting, and pesticide use. From this model, dynamic and sensitivity analyses were carried out, and the optimal control theory was searched using the Pontryagin minimum principle. The analysis results showed three equilibriums: two non-endemic equilibriums (when plant and vector populations exist and when plant, vector, and natural enemy populations exist) and one endemic equilibrium. The non-endemic equilibrium will be asymptotically stable locally if $R_0<1$. At the same time, the parameters that greatly influence the spread of this disease are parameters $\mu , {\mu }_2$, and $\varphi$ for local sensitivity analysis and $\alpha , a, \beta , b, \varphi ,$ and ${\mu }_2$ for global sensitivity analysis. The results of the numerical simulation show that control using combined control is more effective in reducing the intensity of the spread of tungro disease in rice plants than control in the form of planting refugia plants as a source of food for natural enemies. The use of pesticides is sufficient for only four days, so the costs incurred are quite effective in controlling the spread of this disease. Full article

Capturing the factors influencing yellow fever (YF) outbreaks is essential for effective public health interventions, especially in regions like Nigeria, where the disease poses significant health risks. This study explores the synergistic effects of active case detection (ACD) and early hospitalization on controlling YF transmission dynamics. We develop a dynamic model that integrates vaccination, active case detection, and hospitalization to enhance our understanding of disease spread and inform prevention strategies. Our methodology encompasses mechanistic dynamic modeling, optimal control analysis, parameter estimation, model fitting, and sensitivity analyses to study YF transmission dynamics, ensuring the robustness of control measures. We employ advanced mathematical techniques, including next-generation matrix methods, to accurately compute the reproduction number and assess outbreak transmissibility. Rigorous qualitative analysis of the model reveals two equilibria: disease-free and endemic, demonstrating global asymptotic stability and its impact on overall YF transmission dynamics, significantly affecting control and prevention mechanisms. Furthermore, through sensitivity analysis, we identify crucial parameters of the model that require urgent attention for more effective YF control. Moreover, our results highlight the critical roles of ACD and early hospitalization in reducing YF transmission. These insights provide a foundation for informed decision making and resource allocation in epidemic control efforts, ultimately contributing to the enhancement of public health strategies aimed at mitigating the impact of YF outbreaks. Full article

In the face of the COVID-19 pandemic, understanding the dynamics of disease transmission is crucial for effective public health interventions. This study explores the concept of symmetry within compartmental models, employing compartmental analysis and numerical simulations to investigate the intricate interactions between compartments and their implications for disease spread. Our findings reveal the conditions under which the disease-free equilibrium is globally asymptotically stable while the endemic equilibrium exhibits local stability. Additionally, we investigate the phenomenon of backward bifurcation, shedding light on the critical role of quarantine measures in controlling outbreaks. By integrating the concept of symmetry into our model, we enhance our understanding of transmission dynamics and provide a robust framework for evaluating intervention strategies. The insights gained from this research are vital for policymakers and health authorities aiming to mitigate the impact of infectious diseases in the future. Full article

COVID-19 is an enveloped virus with a single-stranded $RNA$ genome. The surface of the virus contains spike proteins, which enable the virus to attach to host cells and enter the interior of the cells. After entering the cell, the virus exploits the host cell’s mechanisms for replication and dissemination. Since the end of 2019, COVID-19 has spread rapidly around the world, leading to a large-scale epidemic. In response to the COVID-19 pandemic, the global scientific community quickly launched vaccine research and development. Vaccination is regarded as a crucial strategy for controlling viral transmission and mitigating severe cases. In this paper, we propose a novel mathematical model for COVID-19 infection incorporating vaccine-induced immunization failure. As a cornerstone of infectious disease prevention measures, vaccination stands as the most effective and efficient strategy for curtailing disease transmission. Nevertheless, even with vaccination, the occurrence of vaccine immunization failure is not uncommon. This necessitates a comprehensive understanding and consideration of vaccine effectiveness in epidemiological models and public health strategies. In this paper, the basic regeneration number is calculated by the next generation matrix method, and the local and global asymptotic stability of disease-free equilibrium point and endemic equilibrium point are proven by methods such as the Routh–Hurwitz criterion and Lyapunov functions. Additionally, we conduct fractional-order numerical simulations to verify that order $0.86$ provides the best fit with COVID-19 data. This study sheds light on the roles of immunization failure and fractional-order control. Full article

In this study, we explore the concept of symmetry as it applies to the dynamics of the Hepatitis B Virus (HBV) epidemic model. By incorporating symmetric principles in the stochastic model, we ensure that the control strategies derived are not only effective but also consistent across varying conditions, and ensure the reliability of our predictions. This paper presents a stochastic optimal control analysis of an HBV epidemic model, incorporating vaccination as a pivotal control measure. We formulate a stochastic model to capture the complex dynamics of HBV transmission and its progression to acute and chronic stages. By leveraging stochastic differential equations, we examine the model’s stationary distribution and asymptotic behavior, elucidating the impact of random perturbations on disease dynamics. Optimal control theory is employed to derive control strategies aimed at minimizing the disease burden and vaccination costs. Through rigorous numerical simulations using the fourth-order Runge–Kutta method, we demonstrate the efficacy of the proposed control measures. Our findings highlight the critical role of vaccination in controlling HBV spread and provide insights into the optimization of vaccination strategies under stochastic conditions. The symmetry within the proposed model equations allows for a balanced approach to analyzing both acute and chronic stages of HBV. Full article

We analyze a time-delayed SIQR model that considers transportation-related infection and entry–exit screening. This model aims to determine the measures for preventing and controlling major emergent infectious diseases and the associated costs. We calculate the basic reproduction number (${\mathcal{R}}_0$) and prove that the disease-free equilibrium is locally and globally asymptotically stable. We collect COVID-19 infection data from two regions in the United States in 2020 for data fitting, obtain a set of optimal parameter values, and find that transportation-related infection rates increase the basic reproduction number, enhancing the impact on disease spread. Entry–exit screening effectively suppresses the spread of disease by reducing the basic reproduction number. Furthermore, we investigate the influence of the incubation period on disease and find that a shorter incubation period results in a shorter duration but a larger scale of infection and that the peaks are reduced. We conduct a sensitivity analysis of the ${\mathcal{R}}_0$ and propose three measures to prevent the spread of new infectious diseases based on the most sensitive parameters: wearing masks, implementing urban closures, and administering medication to sick but not yet hospitalized patients promptly. In the case of COVID-19, optimal control effectively controls the development and deterioration of the disease. Finally, several control measures are compared through cost-effectiveness analysis, and the results show that wearing masks is the most cost-effective measure. Full article