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This work focused on studying the effect of vaccination rate κ on reducing the outbreak of infectious diseases, especially if the infected individuals do not have any symptoms. We employed the fractional order derivative in this study since it has a high degree of accuracy. Recently, a lot of scientists have been interested in fractional-order models. It is considered a modern direction in the mathematical modeling of epidemiology systems. Therefore, a fractional order of the SEIR epidemic model with two types of infected groups and vaccination strategy was formulated and investigated in this paper. The proposed model includes the following classes: susceptible S (t) , exposed E (t) , asymptomatic infected I c (t) , symptomatic infected I η (t) , vaccinated V (t) , and recovered R (t) . We began our study by creating the existence, non-negativity, and boundedness of the solutions of the proposed model. Moreover, we established the basic reproduction number R 0 , that was used to examine the existence and stability of the equilibrium points for the presented model. By creating appropriate Lyapunov functions, we proved the global stability of the free-disease equilibrium point and endemic equilibrium point. We concluded that the free-disease equilibrium point is globally asymptotically stable (GAS) when R 0 ≤ 1 , while the endemic equilibrium point is GAS if R 0 > 1 . Therefore, we indicated the increasing vaccination rate κ leads to reducing R 0 . These findings confirm the important role of vaccination rate κ in fighting the spread of infectious diseases. Moreover, the numerical simulations were introduced to validate theoretical results that are given in this work by applying the predictor-corrector PECE method of Adams-Bashforth-Moulton. Further more, the impact of the vaccination rate κ was explored numerically and we found that, as κ increases, the R 0 is decreased. This means the vaccine can be useful in reducing the spread of infectious diseases. This work focused on studying the effect of vaccination rate on reducing the outbreak of infectious diseases, especially if the infected individuals do not have any symptoms. We employed the fractional order derivative in this study since it has a high degree of accuracy. Recently, a lot of scientists have been interested in fractional-order models. It is considered a modern direction in the mathematical modeling of epidemiology systems. Therefore, a fractional order of the SEIR epidemic model with two types of infected groups and vaccination strategy was formulated and investigated in this paper. The proposed model includes the following classes: susceptible , exposed , asymptomatic infected , symptomatic infected , vaccinated , and recovered . We began our study by creating the existence, non-negativity, and boundedness of the solutions of the proposed model. Moreover, we established the basic reproduction number , that was used to examine the existence and stability of the equilibrium points for the presented model. By creating appropriate Lyapunov functions, we proved the global stability of the free-disease equilibrium point and endemic equilibrium point. We concluded that the free-disease equilibrium point is globally asymptotically stable (GAS) when , while the endemic equilibrium point is GAS if . Therefore, we indicated the increasing vaccination rate leads to reducing . These findings confirm the important role of vaccination rate in fighting the spread of infectious diseases. Moreover, the numerical simulations were introduced to validate theoretical results that are given in this work by applying the predictor-corrector PECE method of Adams-Bashforth-Moulton. Further more, the impact of the vaccination rate was explored numerically and we found that, as increases, the is decreased. This means the vaccine can be useful in reducing the spread of infectious diseases. [ABSTRACT FROM AUTHOR]

This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The prevention and control of the spread of Cystic Echinococcosis is an important public health issue. Health education has been supported by many governments because it can increase public awareness of echinococcosis, promote the development of personal hygiene habits, and subsequently reduce the transmission of echinococcosis. In this paper, a dynamic model of echinococcosis is used to integrate all aspects of health education. Theoretical analysis and numerical model fitting were used to quantitatively analysed by the impact of health education on the spread of echinococcosis. Theoretical findings indicate that the basic reproduction number is crucial in determining the prevalence of echinococcosis within a given geographical area. The parameters of the model were estimated and fitted by using data from the Ningxia Hui Autonomous Region in China, and the sensitivity of the basic reproduction number was analysed by using the partial rank correlation coefficient method. These findings illustrate that all aspects of health education demonstrate a negative correlation with the basic reproduction number, suggesting the effectiveness of health education in reducing the basic reproduction number and mitigating the transmission of echinococcosis, which is consistent with reality. Particularly, the basic reproduction number showed a strong negative correlation with the burial rate of infected livestock (b) and the incidence of infected livestock viscera that is not fed to dogs (q). This paper further analyzes the implementation plan for canine deworming rates and sheep immunity rates, as well as the transmission of infected hosts over time under different parameters b and q. According to the findings, emphasizing the management of infected livestock in health education has the potential to significantly reduce the risk of echinococcosis transmission. This study will provide scientific support for the creation of higher quality health education initiatives. [ABSTRACT FROM AUTHOR]

In this paper, we have delved into the intricate dynamics of a discrete-time Hepatitis B virus (HBV) model, shedding light on its local dynamics, topological classifications at equilibrium states, and pivotal epidemiological parameters such as the basic reproduction number. Our analysis extended to exploring convergence rates, control strategies, and bifurcation phenomena crucial for understanding the behavior of the HBV system. Employing linear stability theory, we meticulously examined the local dynamics of the HBV model, discerning various equilibrium states and their topological classifications. Subsequently, we identified bifurcation sets at these equilibrium points, providing insights into the system’s stability and potential transitions. Further, through the lens of bifurcation theory, we conducted a comprehensive bifurcation analysis, unraveling the intricate interplay of parameters that govern the HBV model’s behavior. Our investigation extended beyond traditional stability analysis to explore chaos and convergence rates, enriching our understanding of the dynamics of the understudied HBV model. Finally, we validated our theoretical findings through numerical simulations, confirming the robustness and applicability of our analysis in real-world scenarios. By integrating biological and epidemiological insights into our mathematical framework, we offered a holistic understanding of the dynamics of HBV transmission dynamics, with implications for public health interventions and disease control strategies. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number R0 is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune responsefree equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection. [ABSTRACT FROM AUTHOR]

Immunotherapy is a targeted therapy that can be applied to cervical cancer patients to prevent DNA damage caused by human papillomavirus (HPV). The HPV infects normal cervical cells withing a specific cell age interval, i.e., between the G1 to S phase of the cell cycle. In this study, we developed a new mathematical model of age-dependent immunotherapy for cervical cancer. The model is a four-dimensional first-order partial differential equation with time- and age-independent variables. The cell population is divided into four sub-populations, i.e., susceptible cells, cells infected by HPV, precancerous cells, and cancer cells. The immunotherapy term has been added to precancerous cells since these cells can experience regression if appointed by proper treatments. The immunotherapy process is closely related to the rate of T-cell division. The treatment works in the same cell cycle that stimulates and inhibits the immune system. In our model, immunotherapy is represented as a periodic function with a small amplitude. It is based on the fluctuating interaction between Tcells and precancerous cells. We have found that there are two types of steady-state conditions, i.e., infection-free and endemic. The local and global stability of an infection-free steady-state has been analyzed based on basic reproduction numbers. We have solved the Riccati differential equation to show the existence of an endemic steady-state. The stability analysis of the endemic steady-state has been determined by using the perturbation approach and solving integral equations. Some numerical simulations are also presented in this paper to illustrate the behavior of the solutions. [ABSTRACT FROM AUTHOR]

In this paper, a fractional order HIV/HTLV co-infection model with HIV-specific antibody immune response is established. Two cases are considered: constant control and optimal control. For the constant control system, the existence and uniqueness of the positive solutions are proved, and then the sufficient conditions for the existence and stability of five equilibriums are obtained. For the second case, the Pontryagin's Maximum Principle is used to analyze the optimal control, and the formula of the optimal solution are derived. After that, some numerical simulations are performed to validate the theoretical prediction. Numerical simulations indicate that in the case of HIV/HTLV co-infection, the concentration of CD4+T cells is no longer suitable as an effective reference data for understanding the development process of the disease. On the contrary, the number of HIV virus particles should be used as an important indicator for reference. [ABSTRACT FROM AUTHOR]

In this paper, we developed a nonlinear mathematical model for the transmission of the monkeypox virus among populations of humans and rodents under the fractal-fractional operators in the context of Atangana-Baleanu. For the theoretical analysis, the renowned theorems of fixed points, like Banach's and Krasnoselskii's types, were used to prove the existence and uniqueness of the solutions. Additionally, some results regarding the stability of the equilibrium points and the basic reproduction number were provided. In addition, the numerical schemes of the considered model were established using the Adams-Bashforth method. Our analytical findings were supported by the numerical simulations to explain the effects of changing a few sets of fractional orders and fractal dimensions. Some graphic simulations were displayed with some parameters calculated from real data to understand the behavior of the model. [ABSTRACT FROM AUTHOR]

Vaccination is widely acknowledged as an affordable and cost-effective approach to guard against infectious diseases. It is important to take vaccination rate, vaccine effectiveness, and vaccine-induced immune decline into account in epidemic dynamical modeling. In this paper, an epidemic dynamical model of vaccination is developed. This model provides a framework of the infectious disease transmission dynamics model through qualitative and quantitative analysis. The result shows that the system may have multiple equilibria. We used the next-generation operator approach to calculate the maximum spectral radius, that is, basic reproduction number Rvac. Next, by dividing the model into infected and uninfected subjects, we can prove that the disease-free equilibrium is globally asymptotically stable when Rvac < 1, provided certain assumptions are satisfied. When Rvac > 1, there exists a unique endemic equilibrium. Using geometric methods, we calculate the second compound matrix and demonstrate the Lozinskii measure ... ≤ 0, which is equivalent to the unique endemic equilibrium, which is globally asymptotically stable. Then, using center manifold theory, we justify the existence of forward bifurcation. As the vaccination rate decreases, the likelihood of forward bifurcation increases. We also theoretically show the presence of Hopf bifurcation. Then, we performed sensitivity analysis and found that increasing the vaccine effectiveness rate can curb the propagation of disease effectively. To examine the influence of vaccination on disease control, we chose the vaccination rate as the optimal vaccination control parameter, using the Pontryagin maximum principle, and we found that increasing vaccination rates reduces the number of infected individuals. Finally, we ran a numerical simulation to finalize the theoretical results. [ABSTRACT FROM AUTHOR]

Nipah virus (NiV) is a zoonotic virus that causes outbreaks of fatal disease in humans. Fruit bat, also known as the flying fox, is the animal host reservoir for NiV. It is known to cause illness in pigs, which are considered an intermediate host. In this paper, we propose a model for NiV disease transmission taking into account all human-to-host animal transmission as well as the loss of immunity in those who have recovered. Furthermore, we take into consideration seasonal effects such as varying transmission rate from bats and birth rate of bats. We studied the existence and uniqueness of a diseasefree ω-periodic solution and later deals with the basic reproduction number and stability analysis. To support the analytical results we provide numerical examples and assess the effect of parameter changes on disease dynamics, which might help to understand how to avoid a yearly periodic recurrence of the disease. [ABSTRACT FROM AUTHOR]

The present paper studies pneumonia transmission dynamics by using fractal-fractional operators in the Atangana-Baleanu sense. Our model predicts pneumonia transmission dynamically. Our goal is to generalize five ODEs of the first order under the assumption of five unknowns (susceptible, vaccinated, carriers, infected, and recovered). The Atangana-Baleanu operator is used in addition to analysing existence, uniqueness, and non-negativity of solutions, local and global stability, Hyers-Ulam stability, and sensitivity analysis. As long as the basic reproduction number R0 is less than one, the free equilibrium point is local, asymptotic, or otherwise global. Our sensitivity statistical analysis shows that R0 is most sensitive to pneumonia disease density. Further, we compute a numerical solution for the model by using fractal-fractional. Graphs of the results are presented for demonstration of our proposed method. The results of the Atangana-Baleanu fractal-fractional scheme is in excellent agreement with the actual data. [ABSTRACT FROM AUTHOR]

The host population in epidemiology may actually be at risk of more than two infectious diseases with stochastic complicated interaction, e.g., HIV and HBV. In this paper, we propose a class of stochastic epidemic model that applies the double epidemic hypothesis and Crowley-Martin incidence rate in order to explore how stochastic disturbances affect the spread of diseases. While disregarding stochastic disturbances, we examine the dynamic features of the system in which the local stability of equilibria are totally determined by the basic reproduction numbers. We focus particularly on the threshold dynamics of the corresponding stochastic system, and we obtain the extinction and permanency conditions for a pair of infectious diseases. We find that the threshold dynamics of the deterministic and stochastic systems vary significantly: (ⅰ) disease outbreaks can be controlled by appropriate stochastic disturbances; (ⅱ) diseases die out when the intensity of environmental perturbations is higher. The effects of certain important parameters on deterministic and stochastic disease transmission were obtained through numerical simulations. Our observations indicate that controlling epidemics should improve the effectiveness of prevention measures for susceptible individuals while improving the effectiveness of treatment for infected individuals. [ABSTRACT FROM AUTHOR]

The chikungunya virus (CHIKV) infects macrophages and adherent cells and it can be transmitted via a direct contact with the virus or with an already infected cell. Thus, the CHIKV infection can have two routes. Furthermore, it can exhibit seasonal peak periods. Thus, in this paper, we consider a dynamical system model of the CHIKV dynamics under the conditions of a seasonal environment with a general incidence rate and two routes of infection. In the first step, we studied the autonomous system by investigating the global stability of the steady states with respect to the basic reproduction number. In the second step, we establish the existence, uniqueness, positivity and boundedness of a periodic orbit for the non-autonomous system. We show that the global dynamics are determined by using the basic reproduction number denoted by R0 and they are calculated using the spectral radius of an integral operator. We show the global stability of the disease-free periodic solution if R0 < 1 and we also show the persistence of the disease if R0 > 1 where the trajectories converge to a limit cycle. Finally, we display some numerical investigations supporting the theoretical findings. [ABSTRACT FROM AUTHOR]

Anthrax is a bacterial infection caused by Bacillus anthracis, primarily affecting animals and occasionally affecting humans. This paper presents two compartmental deterministic models of anthrax transmission having vaccination compartments. In both models, a nonlinear ratio-dependent disease transmission function is employed, and the latter model distinguishes itself by incorporating fractional order derivatives, which adds a novel aspect to the study. The basic reproduction number R0 of the epidemic is determined, below which the disease is eradicated. It is observed that among the various parameters, the contact rate, disease-induced mortality rate, and rate of animal recovery have the potential to influence this basic reproduction number. The endemic equilibrium becomes diseasefree via transcritical bifurcations for different threshold parameters of animal recovery rate, disease-induced mortality rate and disease transmission rate, which is validated by utilizing Sotomayor's theorem. Numerical simulations have revealed that a higher vaccination rate contributes to eradicating the disease within the ecosystem. This can be achieved by effectively controlling the disease-induced death rate and promoting animal recovery. The extended fractional model is analyzed numerically using the Adams-Bashforth-Moulton type predictor-corrector scheme. Finally, it is observed that an increase in the fractional order parameter has the potential to reduce the time duration required to eradicate the disease from the ecosystem. [ABSTRACT FROM AUTHOR]

Several mathematical models of two competing viruses (or viral strains) that have been published in the literature assume that the infection rate is determined by bilinear incidence. These models do not show co-existence equilibrium; moreover, they might not be applicable in situations where the virus concentration is high. In this paper, we developed a mathematical model for the co-dynamics of two competing viruses with saturated incidence. The model included the latently infected cells and three types of time delays: discrete (or distributed): (i) The formation time of latently infected cells; (ii) The activation time of latently infected cells; (iii) The maturation time of newly released virions. We established the mathematical well-posedness and biological acceptability of the model by examining the boundedness and nonnegativity of the solutions. Four equilibrium points were identified, and their stability was examined. Through the application of Lyapunov's approach and LaSalle's invariance principle, we demonstrated the global stability of equilibria. The impact of saturation incidence, latently infected cells, and time delay on the viral co-dynamics was examined. We demonstrated that the saturation could result in persistent viral coinfections. We established conditions under which these types of viruses could coexist. The coexistence conditions were formulated in terms of saturation constants. These findings offered new perspectives on the circumstances under which coexisting viruses (or strains) could live in stable viral populations. It was shown that adding the class of latently infected cells and time delay to the coinfection model reduced the basic reproduction number for each virus type. Therefore, fewer treatment efficacies would be needed to keep the system at the infection-free equilibrium and remove the viral coinfection from the body when utilizing a model with latently infected cells and time delay. To demonstrate the associated mathematical outcomes, numerical simulations were conducted for the model with discrete delays. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts. [ABSTRACT FROM AUTHOR]

In this paper, we develop a mathematical model for the spread of COVID-19 outbreak, taking into account vaccination in susceptible and recovered populations. The model divides the population into eight classes, including susceptible, vaccinated in S class, exposed, infected asymptomatic, infected symptomatic, hospitalized, recovery, and vaccinated in recovered class. By applying a vaccine-distribution scenario, we investigate the impact of vaccines on the COVID-19 outbreak. After analyzing the equilibrium point and computing the basic reproduction number, we perform numerical simulation and sensitivity analysis to identify the most influential parameters and evaluate the impact of vaccine distribution on policies to control the spread of COVID-19. Our findings suggest that vaccine distribution can effectively suppress the spread of COVID-19, and increasing the v parameter (vaccine distribution) and α 1 parameter (acceleration of detection of undetected infected individuals who have recovered) can help control the outbreak. Moreover, decreasing the contact between vulnerable and infected individuals can lower the β 1 parameter, leading to R 0 < 1 , which indicates a disease-free population. This study contributes to understanding the impact of vaccination on the spread of COVID-19 and provides insights for policymakers in developing control strategies. [ABSTRACT FROM AUTHOR]

Infectious diseases have a great impact on the economy and society. Dynamic models of infectious diseases are an effective tool for revealing the laws of disease transmission. Quarantine and nonlinear innate immunity are the crucial factors in the control of infectious diseases. Currently, there no mathematical models that comprehensively study the effect of both innate immunity and quarantine. In this paper, we propose and analyze an SEIQR epidemic model with nonlinear innate immunity. The boundedness and positivity of the solutions are discussed. Employing the next-generation matrix, we compute the expression of the basic reproduction number. Under certain conditions, the phenomenon of backward bifurcation may occur. That is to say, the stable disease-free equilibrium point and the stable endemic equilibrium point coexist when the basic reproduction ratio is less than one. And the basic reproduction number is no longer the threshold value to determine whether the disease breaks out. We investigate the globally asymptotical stability of the disease-free equilibrium point for the system by constructing Lyapunov function. Also, we research the global stability of the endemic equilibrium by using geometric approach. Numerical simulations are carried out to reveal the theoretical results and find some complex dynamics (for example, the existence of Hopf bifurcation) of the system. Both theoretical and numerical results indicate that the nonlinear innate immunity may cause backward bifurcation and Hopf bifurcation, which makes more difficult to eliminate the disease. [ABSTRACT FROM AUTHOR]

The spread of rumors is a phenomenon that has heavily impacted society for a long time. Recently, there has been a huge change in rumor dynamics, through the advent of the Internet. Today, online communication has become as common as using a phone. At present, getting information from the Internet does not require much effort or time. In this paper, the impact of the Internet on rumor spreading will be considered through a simple SIR type ordinary differential equation. Rumors spreading through the Internet are similar to the spread of infectious diseases through water and air. From these observations, we study a model with the additional principle that spreaders lose interest and stop spreading, based on the SIWR model. We derive the basic reproduction number for this model and demonstrate the existence and global stability of rumor-free and endemic equilibriums. [ABSTRACT FROM AUTHOR]

COVID-19 has become a serious pandemic affecting many countries around the world since it was discovered in 2019. In this research, we present a compartmental model in ordinary differential equations for COVID-19 with vaccination, inflow of infected and a generalized contact rate. Existence of a unique global positive solution of the model is proved, followed by stability analysis of the equilibrium points. A control problem is presented, with vaccination as well as reduction of the contact rate by way of education, law enforcement or lockdown. In the last section, we use numerical simulations with data applicable to South Africa, for supporting our theoretical results. The model and application illustrate the interesting manner in which a diseased population can be perturbed from within itself. [ABSTRACT FROM AUTHOR]

A nonautonomous mathematical model was presented to explore the complex dynamics of disease spread over time, incorporating a time-periodic transmission parameter and imperfections in quarantine, isolation and vaccination strategies. Through a detailed examination of threshold dynamics, it was revealed that the global dynamics of disease transmission are influenced by the basic reproduction number (R0), a critical threshold that determines extinction, persistence, and the presence of periodic solutions. It was shown that the disease-free equilibrium is globally asymptotically stable if R0 < 1, while the disease persists if R0 > 1. To support and validate our analytical results, the basic reproduction number and the dynamics of the disease were estimated by fitting monthly data from two Asian countries, namely Saudi Arabia and Pakistan. Furthermore, a sensitivity analysis of the time-averaged reproduction number (R0) of the associated time-varying model showed a significant sensitivity to key parameters such as infection rates, quarantine rate, vaccine coverage rate, and recovery rates, supported by numerical simulations. These simulations validated theoretical findings and explored the impact of seasonal contact rate, imperfect quarantine, isolation, imperfect vaccination, and other parameters on the dynamics of measles transmission. The results showed that increasing the rate of immunization, improving vaccine management, and raising public awareness can reduce the incidence of the epidemic. The study highlighted the importance of understanding these patterns to prevent future periodic epidemics. [ABSTRACT FROM AUTHOR]

The spread of rumors has an important impact on the production and life of human society. Moreover, in the process of rumor propagation, individuals with different educational levels show different degrees of trust and ability to spread rumors. Therefore, a new rumor propagation model was established, which considers the influence of education level on rumor propagation. Initially, the basic reproduction number of the model was calculated. Then, we analyzed the existence and stability of the rumor equilibrium point. Next, based on the principle of Pontryagin's maximum value, we obtained a control strategy, which effectively reduced the spread of rumors. Numerical simulations verified the results of theoretical analysis. The results showed that the higher the education level of the population, the slower the spread of rumors to a certain extent, but it could not prevent the spread of rumors. In addition, through the support of the government and the propaganda of the official media, strengthening education can improve people's education level to a certain extent, and then minimize the speed of rumor propagation. [ABSTRACT FROM AUTHOR]

In order to study the impact of seasonality on Zika virus dynamics, we analyzed a non-autonomous mathematical model for the Zika virus (ZIKV) transmission where we considered time-dependent parameters. We proved that the system admitted a unique bounded positive solution and a global attractor set. The basic reproduction number, R0, was defined using the next generation matrix method for the case of fixed environment and as the spectral radius of a linear integral operator for the case of seasonal environment. We proved that if R0 was smaller than the unity, then a disease-free periodic solution was globally asymptotically stable, while if R0 was greater than the unity, then the disease persisted. We validated the theoretical findings using several numerical examples. [ABSTRACT FROM AUTHOR]

Coronavirus spread in Wuhan, China, in December 2019. A few weeks later, the virus was present in over 100 countries around the globe. Governments have adopted extreme measures to contain the spreading virus. Quarantine is considered the most effective way to control the spreading speed of COVID-19. In this study, a mathematical model is developed to explore the influence of quarantine and the latent period on the spatial spread of COVID-19. We use the mathematical model with quarantine, and delay to predict the spreading speed of the virus. In particular, we transform the model to a single integral equation and then apply the Laplace transform to find implicit equations for the spreading speeds. The basic reproduction number of COVID-19 is also found and calculated. Numerical simulations are performed to confirm our theoretical results. To validate the proposed model, we compare our outcomes with the actual reported data published by the National Health Commission of China and the Health Commission of local governments. The model demonstrates good qualitative agreement with the actual data reported. The results show that delay and quarantine highly influence the spreading speeds of COVID-19. Also, we can only contain the disease if we quarantine 75% of the infected people. [ABSTRACT FROM AUTHOR]

In order to study the effects of reverse transcriptase inhibitors, protease inhibitors and flavonoids on two target cells infected by HIV in a heterogeneous environment, an HIV mathematical model at the cellular level was established. Research shows that infected cells can be categorized into immature infected cells, latent infected cells, and mature infected cells based on the infection process. The basic reproduction number R 0 was established, and it is proved that R 0 serves as a threshold parameter: When R 0 < 1 , the disease-free steady state is globally asymptotically stable, and the disease is extinct; when R 0 > 1 , the solution of the system is uniformly persistent, and the virus exists. Considering the huge advantages of drug intervention in controlling HIV infection, the optimal control problem was proposed under the condition that the constant diffusion coefficient is positive, so as to minimize the total number of HIV-infected cells and the cost of drug treatment. To illustrate our theoretical results, we performed numerical simulations in which the model parameters were obtained with reference to some medical studies. The results showed that: (1) as R 0 increases, the risk of HIV transmission increases; (2) pharmacological interventions are important in early treatment of HIV spread and control of viral load in the body; (3) the treatment process must consider the heterogeneity of medication, otherwise it will not be conducive to suppressing the spread of the virus and will increase costs. In order to study the effects of reverse transcriptase inhibitors, protease inhibitors and flavonoids on two target cells infected by HIV in a heterogeneous environment, an HIV mathematical model at the cellular level was established. Research shows that infected cells can be categorized into immature infected cells, latent infected cells, and mature infected cells based on the infection process. The basic reproduction number was established, and it is proved that serves as a threshold parameter: When , the disease-free steady state is globally asymptotically stable, and the disease is extinct; when , the solution of the system is uniformly persistent, and the virus exists. Considering the huge advantages of drug intervention in controlling HIV infection, the optimal control problem was proposed under the condition that the constant diffusion coefficient is positive, so as to minimize the total number of HIV-infected cells and the cost of drug treatment. To illustrate our theoretical results, we performed numerical simulations in which the model parameters were obtained with reference to some medical studies. The results showed that: (1) as increases, the risk of HIV transmission increases; (2) pharmacological interventions are important in early treatment of HIV spread and control of viral load in the body; (3) the treatment process must consider the heterogeneity of medication, otherwise it will not be conducive to suppressing the spread of the virus and will increase costs. [ABSTRACT FROM AUTHOR]

Recent studies have demonstrated the superiority of cell-to-cell transmission over cellfree virus infection, and highlighted the role of inflammatory cytokines in enhancing viral infection. To investigate their impacts on viral infection dynamics, we have proposed an HIV infection model incorporating general incidence rates, these infection modes, and two time delays. We derived the basic reproduction number and showed that it governs the existence and local stability of steady states. Through the construction of appropriate Lyapunov functionals and application of the LaSalle invariance principle, we established the global asymptotic stability of both the infection-free and infected steady states. [ABSTRACT FROM AUTHOR]

Dengue is a viral illness transmitted by Aedes mosquitoes and is a significant global threat. In this study, we developed a model of the dengue epidemic that incorporates larvicide and adulticide, as well as the harmonic mean incidence rate under fractal-fractional derivatives. We examined various theoretical aspects of the model, including nonnegativity, boundedness, existence, uniqueness, and stability. We computed the basic reproduction number R0 using the next-generation matrix. The model has two disease-free equilibriums, a trivial equilibrium, and a biologically realistic, along with one endemic equilibrium point. These findings enhanced our understanding of dengue transmission, providing valuable insights for awareness campaigns, control strategies, intervention approaches, decision support, guiding public health planning, and resource allocation to manage dengue effectively. [ABSTRACT FROM AUTHOR]

This study presents a mathematical model capturing Malaria transmission dynamics in Yemen, incorporating a social hierarchy structure. Piecewise Caputo-Fabrizio derivatives are utilized to effectively capture intricate dynamics, discontinuities, and different behaviors. Statistical data from 2000 to 2021 is collected and analyzed, providing predictions for Malaria cases in Yemen from 2022 to 2024 using Eviews and Autoregressive Integrated Moving Average models. The model investigates the crossover effect by dividing the study interval into two subintervals, establishing existence, uniqueness, positivity, and boundedness of solutions through fixed-point techniques and fractional-order properties of the Laplace transformation. The basic reproduction number is computed using a next-generation technique, and numerical solutions are obtained using the Adams-Bashforth method. The results are comprehensively discussed through graphs. The obtained results can help us to better control and predict the spread of the disease. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is an infectious disease transmitted through the respiratory system. China is one of the countries with a high burden of TB. Since 2004, an average of more than 800,000 cases of active TB has been reported each year in China. Analyzing the case data from 2004 to 2018, we found significant differences in TB incidence by age group. A model of TB is put forward to explore the effect of age heterogeneity on TB transmission. The nonlinear least squares method is used to obtain the key parameters in the model, and the basic reproduction number Rv = 0.8017 is calculated and the sensitivity analysis of Rv to the parameters is given. The simulation results show that reducing the number of new infections in the elderly population and increasing the recovery rate of elderly patients with the disease could significantly reduce the transmission of TB. Furthermore, the feasibility of achieving the goals of the World Health Organization (WHO) End TB Strategy in China is assessed, and we obtained that with existing TB control measures it will take another 30 years for China to reach the WHO goal to reduce 90% of the number of new cases by the year 2049. However, in theory it is feasible to reach the WHO strategic goal of ending TB by 2035 if the group contact rate in the elderly population can be reduced, though it is difficult to reduce the contact rate. [ABSTRACT FROM AUTHOR]

A mathematical model is developed for analysis of the spread of mosaic disease in plants, which account for incubation period and latency that are represented by time delays. Feasibility and stability of different equilibria are studied analytically and numerically. Conditions that determine the type of behavior exhibited by the system are found in terms of various parameters. We have derived the basic reproduction number and identify the conditions resulting in eradication of the disease, as well as those that lead to the emergence of stable oscillations in the population of infected plants, as a result of Hopf bifurcation of the endemic equilibrium. Numerical simulations are performed to verify the analytical results and also to illustrate different dynamical regimes that can be observed in the system. In this research, the stabilizing role of both the time delay has been established i.e. when delay time is large, disease will persist if the infection rate is higher. The results obtained here are useful for plant disease management. [ABSTRACT FROM AUTHOR]

To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell andWilliams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a possible quarantine of the infectious individuals. We provide an analytic description of this Markovian model and investigate its dynamics. Both a diffusion approximation and the basic reproduction number are derived. Through several simulations, we show how the evolution of a disease is affected by the distribution of the number of daily encounters and its dependence on time. Finally, we show how the appropriate choice of this parameter allows a suitable application of our model to two real diseases. [ABSTRACT FROM AUTHOR]

In this study, we investigated the threshold dynamics of a spatially heterogeneous nonlocal diffusion West Nile virus model. By employing semigroup theory and continuous Fréchet-differentiable, we established the well-posedness of the solution. The expression for the basic reproduction number derived using the next-generation matrix method. The authors demonstrated the threshold dynamics of the system by constructing a Lyapunov function and applying the comparison principle. Finally, numerical simulations were used to validate the theorem results. It can be suggested that to control disease development rapidly, measures should be taken to reduce the spread of mosquitoes and birds. [ABSTRACT FROM AUTHOR]

It is valuable to measure the epidemiological significance of malaria, since there has been a growing interest in reducing malaria through improved local and national health care systems. We formulate the dynamics of malaria infection via a fractional framework to understand the intricate transmission route of malaria and to identify the role of memory for the control of malaria. The model is investigated for basic results, moreover, the basic reproduction number is determined symbolized by R0. We have shown the local stability of the disease-free steady-state of the system for for R0 < 1. The existence and uniqueness of the solution of the system are examined. The Adams Bashforth approach in fractional form is applied to analyse the numerical outcomes of the mathematical model. Furthermore, in order to realise more efficiently, the Atangana-Baleanu (ABC) fractional nonlocal operator, which was just invented, is used. The stability of the system is investigated through the fixed-point theorems of Krasnoselskii and Banach. The behaviour of the approximation solution is illustrated in terms of graphs across various fractional values and other factors of the systems. After all, a brief analysis of the simulation's findings is provided to explain how infection transmission dynamics occur in society. [ABSTRACT FROM AUTHOR]

In this manuscript, we are proposing a new kind of modified Susceptible Exposed Infected Quarantined Recovered model (SEIQR) with some assumed data. The novelty imposed here in the study is that we are studying simultaneously SIR, SEIR, SIQR, and SEQR pandemic models with the same data unchanged as the SEIQR model. We are taking this model a step ahead by using a nonhelpful transition because it was mostly skipped in the literature. All sorts of features that are essential to study the models, such as basic reproduction number, stability analysis, and numerical simulations have been examined for this modified SEIQR model with decomposed other epidemic models. [ABSTRACT FROM AUTHOR]

The use of vaccines has always been controversial. Individuals in society may have different opinions about the benefits of vaccines. As a result, some people decide to get vaccinated, while others decide otherwise. The conflicting opinions about vaccinations have a significant impact on the spread of a disease and the dynamics of an epidemic. This study proposes a mathematical model of COVID-19 to understand the interactions of two populations: the low risk population and the high risk population, with two preventive measures. Unvaccinated individuals with chronic diseases are classified as high risk population while the rest are a low risk population. Preventive measures used by low risk group include vaccination (pharmaceutical way), while for the high risk population they include wearing masks, social distancing and regular hand washing (non-pharmaceutical ways). The susceptible and infected sub-populations in both the low risk and the high risk groups were studied in detail through calculations of the effective reproduction number, model analysis, and numerical simulations. Our results show that the introduction of vaccination in the low risk population will significantly reduce infections in both subgroups. [ABSTRACT FROM AUTHOR]

Mathematical modelling has been widely used in many fields, especially in recent years. The applications of mathematical modelling in infectious diseases have shown that situations such as isolation, quarantine, vaccination and treatment are often necessary to eliminate most infectious diseases. In this study, a mathematical model of COVID-19 disease involving susceptible (S), exposed (E), infected (I), quarantined (Q), vaccinated (V) and recovered (R) populations is considered. In order to show the biological significance of the system, the non-negative solution region and the boundedness of the relevant biological compartments are shown. The endemic and disease-free equilibrium points of the model are calculated, and local stability analyses of these equilibrium points are performed. The basic reproduction number is also calculated for the relevant model. Sensitivity analysis of this number is studied, and it has been pointed out which parameters affect this number and how they affect it. Moreover, using real data from Iraq, the model parameters are estimated using the least squares curve fitting method, and numerical simulations are performed by using these estimated values. For the solution of the model, the Adams-Bashforth type predictive-corrective numerical method is used, and with the help of numerical simulations, several predictions are achieved about the future course of COVID-19. [ABSTRACT FROM AUTHOR]

The current emergence of coronavirus (SARS-CoV-2 or COVID-19) has put the world in threat. Social distancing, quarantine and governmental measures such as lockdowns, social isolation, and public hygiene are helpful in fighting the pandemic, while awareness campaigns through social media (radio, TV, etc.) are essential for their implementation. On this basis, we propose and analyse a mathematical model for the dynamics of COVID-19 transmission influenced by awareness campaigns through social media. A time delay factor due to the reporting of the infected cases has been included in the model for making it more realistic. Existence of equilibria and their stability, and occurrence of Hopf bifurcation have been studied using qualitative theory. We have derived the basic reproduction number (R0) which is dependent on the rate of awareness. We have successfully shown that public awareness has a significant role in controlling the pandemic. We have also seen that the time delay destabilizes the system when it crosses a critical value. In sum, this study shows that public awareness in the form of social distancing, lockdowns, testing, etc. can reduce the pandemic with a tolerable time delay. [ABSTRACT FROM AUTHOR]