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A time-delayed virus dynamic model is proposed with general monotonic incidence, different nonlinear CTL (cytotoxic T lymphocyte) responses [CTL elimination function p y g 1 (z) and CTL stimulation function c y g 2 (z) ], and immune impairment. Indeed, the different CTL responses pose challenges in obtaining the dissipativeness of the model. By constructing appropriate Lyapunov functionals with some detailed analysis techniques, the global stability results of all equilibria of the model are obtained. By the way, we point out that the partial derivative f v (x , 0) is increasing (but not necessarily strictly) in x > 0 for the general monotonic incidence f (x , v). However, some papers defaulted that the partial derivative was strictly increasing. Our main results show that if the basic reproduction number R 0 ≤ 1 , the infection-free equilibrium E 0 is globally asymptotically stable (GAS); if CTL stimulation function c y g 2 (z) = 0 for z = 0 and the CTL threshold parameter R 1 ≤ 1 < R 0 , then the immunity-inactivated infection equilibrium E 1 is GAS; if the immunity-activated infection equilibrium E + exists, then it is GAS. Two specific examples are provided to illustrate the applicability of the main results. The main results acquired in this paper improve or extend some of the existing results. [ABSTRACT FROM AUTHOR]

In this paper, a new stochastic epidemic model is established and the dynamical behavior of its solutions is studied for this model. A deterministic epidemic model (ordinary differential equation) is first proposed by considering the isolation mechanism, and the transmission probability function is determined by a Wells–Riley model method to analyze the transmission in the quarantine. For this deterministic model, the basic reproduction number R 0 is computed and it is used to determine the existence of disease-free and positive equilibria. The linearized stability of the equilibria is also discussed by analyzing the distribution of eigenvalues of the linear system. Following that, a corresponding stochastic epidemic model is further established by introducing stochastic disturbance. Then, the extinction result of the model is derived also with the help of the basic reproduction number R 0 s. Furthermore, by applying the theory of Markov semigroups, it is proved that the densities of the distributions of the solutions can converge to an invariant density or sweeping under certain conditions. At last, some numerical simulations are provided and discussed to illustrate the practicability of the model and the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a reaction–diffusion–chemotaxis HIV-1 model with a cytotoxic T lymphocyte (CTL) immune response and general sensitivity is investigated. We first prove the global classical solvability and L ∞ -boundedness for the considered model in a bounded domain with arbitrary spatial dimensions, which extends the previous existing results. Then, we apply the global existence result to the case with a linear proliferation immune response and an incidence rate. We study the spatiotemporal dynamics about the three types of spatially homogeneous steady states: infection-free steady state S 0 , CTL-inactivated infection steady state S 1 , and CTL-activated infection steady state S ∗. Our analyses indicate that S 0 is globally asymptotically stable if the basic reproduction number R 0 is less than 1; if R 0 is between 1 and a threshold, then S 1 is globally asymptotically stable. However, if R 0 is larger than the threshold, then the chemoattraction and chemorepulsion can destabilize S ∗ , and thus, a spatiotemporal pattern forms as the chemotactic sensitivity crosses certain critical values. We obtain two kinds of important patterns, which are induced by chemotaxis: stationary Turing pattern and irregular oscillatory pattern. We also find that different chemotactic response functions can affect system's dynamics. Based on some empirical parameter values, numerical simulations are given to illustrate the effectiveness of the theoretical predications. [ABSTRACT FROM AUTHOR]

In this research paper, a novel approach in dengue modeling with the asymptomatic carrier and reinfection via the fractional derivative is suggested to deeply interrogate the comprehensive transmission phenomena of dengue infection. The proposed system of dengue infection is represented in the Liouville–Caputo fractional framework and investigated for basic properties, that is, uniqueness, positivity, and boundedness of the solution. We used the next-generation technique in order to determine the basic reproduction number R 0 for the suggested model of dengue infection; moreover, we conduct a sensitivity test of R 0 through a partial rank correlation coefficient technique to know the contribution of input factors on the output of R 0. We have shown that the infection-free equilibrium of dengue dynamics is globally asymptomatically stable for R 0 < 1 and unstable in other circumstances. The system of dengue infection is then structured in the Atangana–Baleanu framework to represent the dynamics of dengue with the non-singular and non-local kernel. The existence and uniqueness of the solution of the Atangana–Baleanu fractional system are interrogated through fixed-point theory. Finally, we present a novel numerical technique for the solution of our fractional-order system in the Atangana–Baleanu framework. We obtain numerical results for different values of fractional-order ϑ and input factors to highlight the consequences of fractional-order ϑ and input parameters on the system. On the basis of our analysis, we predict the most critical parameters in the system for the elimination of dengue infection. [ABSTRACT FROM AUTHOR]

Foot-and-mouth disease is a highly contagious and economically devastating disease of cloven-hoofed animals. The historic occurrences of foot-and-mouth diseases led to huge economic losses and seriously threatened the livestock food security. In this paper, a novel age-space diffusive foot-and-mouth disease model with a Dirichlet boundary condition, coupling the virus-to-animals and animals-to-animals transmission routes, has been proposed. The basic reproduction number R 0 is defined as the spectral radius of a next generation operator K , which is calculated in an explicit form, and it serves as a vital value determining whether or not the disease persists. The existence of a unique trivial nonconstant steady state and at least one nonconstant endemic steady state of the system is established by a smart Lyapunov functional and the Kronoselskii fixed point theorem. An application to a foot-and-mouth outbreak in China is presented. The findings suggest that increasing the movements and disinfection of the environment for animals apparently reduce the risk of a foot-and-mouth infection. [ABSTRACT FROM AUTHOR]

This paper describes the existence and stability of the hepatitis B epidemic model with a fractional-order derivative in Atangana–Baleanu sense. Some new results are handled by using the Sumudu transform. The existence and uniqueness of the equilibrium solution are presented using the Banach fixed-point theorem. Moreover, sensitivity analysis complemented by simulations is performed to determine how changes in parameters affect the dynamical behavior of the system. The numerical simulations are carried out using a predictor-corrector scheme to demonstrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a concise method to investigate the global dynamics of a mean-field vector-borne diseases model on complex networks. We obtain an explicit formula of the basic reproduction number by a renewal equation. We show that the model exhibits a threshold dynamics in terms of the basic reproduction number by constructing subtle Lyapunov functions. Roughly speaking, if the basic reproduction number R 0 < 1 , the vector-borne diseases die out; otherwise, it persists. Moreover, numerical simulations show that vector-control is an effective measure for slowing down the spread of vector-borne diseases. [ABSTRACT FROM AUTHOR]

The ongoing monkeypox outbreak that began in the UK has currently spread to every continent. Here, we use ordinary differential equations to build a nine-compartmental mathematical model to examine the dynamics of monkeypox transmission. The basic reproduction number for both humans ( R 0 h) and animals ( R 0 a) is obtained using the next-generation matrix technique. Depending on the values of R 0 h and R 0 a , we discovered that there are three equilibria. The current study also looks at the stability of all equilibria. We discovered that the model experiences transcritical bifurcation at R 0 a = 1 for any value of R 0 h and at R 0 h = 1 for R 0 a < 1. This is the first study that, to the best of our knowledge, has constructed and solved an optimal monkeypox control strategy while taking vaccination and treatment controls into consideration. The infected averted ratio and incremental cost-effectiveness ratio were calculated to evaluate the cost-effectiveness of all viable control methods. Using the sensitivity index technique, the parameters used in the formulation of R 0 h and R 0 a are scaled. [ABSTRACT FROM AUTHOR]

A fractional order susceptible–exposed–infected–quarantined–recovered model is established on the complex networks. We calculate a specific expression for the basic reproduction number R 0 , prove the existence and uniqueness with respect to the solution, and prove the Ulam–Hyers stability of the model. Using the Latin hypercube sampling-partial rank correlation coefficient method, the influence of parameters on the R 0 is analyzed. Based on the results of the analysis, the optimal control of the model is investigated as the control variables with vaccination rate and quarantine rate applying Pontryagin's minimum principle. The effects of α , degree of nodes, and network size on the model dynamics are simulated separately by the prediction correction method. [ABSTRACT FROM AUTHOR]

Bovine viral diarrhea (BVD) is a disease in cattle with complex transmission dynamics that causes substantial economic losses and affects animal welfare. The infection can be transient or persistent. The mostly asymptomatic persistently infected hosts are the main source for transmission of the virus. This characteristic makes it difficult to control the spreading of BVD. We develop a deterministic compartmental model for the spreading dynamics of BVD within a herd and derive the basic reproduction number. This epidemiological quantity indicates that identification and removal of persistently infected animals is a successful control strategy if the transmission rate of transiently infected animals is small. Removing persistently infected animals from the herd at birth results in recurrent outbreaks with decreasing peak prevalence. We propose a stochastic version of the compartmental model that includes stochasticity in the transmission parameters. This stochasticity leads to sustained oscillations in cases where the deterministic model predicts oscillations with decreasing amplitude. The results provide useful information for the design of control strategies. [ABSTRACT FROM AUTHOR]

We propose a Lévy noise-driven susceptible-exposed-infected-recovered model incorporating media coverage to analyze the outbreak of COVID-19. We conduct a theoretical analysis of the stochastic model by the suitable Lyapunov function, including the existence and uniqueness of the positive solution, the dynamic properties around the disease-free equilibrium and the endemic equilibrium; we deduce a stochastic basic reproduction number R 0 s for the extinction of disease, that is, if R 0 s ≤ 1 , the disease will go to extinction. Particularly, we fit the data from Brazil to predict the trend of the epidemic. Our main findings include the following: (i) stochastic perturbation may affect the dynamic behavior of the disease, and larger noise will be more beneficial to control its spread; (ii) strengthening social isolation, increasing the cure rate and media coverage can effectively control the spread of disease. Our results support the feasible ways of containing the outbreak of the epidemic. [ABSTRACT FROM AUTHOR]

In order to depict a situation of possible spread of infection from prey to predator, a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness, and existence of the solutions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model, and in terms of these threshold parameters, we have derived some conditions for the stability of these equilibrium points. Global stability of axial, predator-extinct, and disease-free equilibrium points are investigated. Novelty of this model is that fractional derivative is incorporated in a system where susceptible predators get the infection from preys while predating as well as from infected predators and both infected preys and predators do not reproduce. The occurrences of transcritical bifurcation for the proposed model are investigated. By finding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased preys allows us to eliminate the disease from the environment, otherwise the disease would have remained endemic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator, and infected predator populations. Numerical computations are conducted to strengthen the theoretical findings. [ABSTRACT FROM AUTHOR]

When a disease spreads in a population, individuals tend to change their behavior due to the presence of information about disease prevalence. Therefore, the infection rate is affected and incidence term in the model should be appropriately modified. In addition, a limitation of medical resources has its impact on the dynamics of the disease. In this work, we propose and analyze an Susceptible-Exposed-Infected-Recovered (SEIR) model, which accounts for the information-induced non-monotonic incidence function and saturated treatment function. The model analysis is carried out, and it is found that when R 0 is below one, the disease may or may not die out due to the saturated treatment (i.e., a backward bifurcation may exist and cause multi-stability). Further, we note that in this case, disease eradication is possible if medical resources are available for all. When R 0 exceeds one, there is a possibility of the existence of multiple endemic equilibria. These multiple equilibria give rise to rich and complex dynamics by showing various bifurcations and oscillations (via Hopf bifurcation). A global asymptotic stability of a unique endemic equilibrium (when it exists) is established under certain conditions. An impact of information is shown and also a sensitivity analysis of model parameters is performed. Various cases are considered numerically to provide the insight of model behavior mathematically and epidemiologically. We found that the model shows hysteresis. Our study underlines that a limitation of medical resources may cause bi(multi)-stability in the model system. Also, information plays a significant role and gives rise to a rich and complex dynamical behavior of the model. [ABSTRACT FROM AUTHOR]

In this study, an individual-based model is proposed to investigate the effect of demographic stochasticity on biological control using entomopathogenic fungi. The model is formulated as a continuous time Markov process, which is then decomposed into a deterministic dynamics using stochastic corrections and system size expansion. The stability and bifurcation analysis shows that the system dynamic is strongly affected by the contagion rate and the basic reproduction number. However, sensitivity analysis of the extinction probability shows that the persistence of a biological control agent depends to the proportion of spores collected from insect cadavers as well as their ability to be reactivated and infect insects. When considering the migration of each species within a set of patches, the dispersion relation shows a Hopf-damped Turing mode for a threshold contagion rate. A large size population led to a spatial and temporal resonant stochasticity and also induces an amplification effect on power spectrum density. [ABSTRACT FROM AUTHOR]

The study of epidemics spreading with community structure has become a hot topic. The classic S I R epidemic model does not distinguish between dead and recovered individuals. It is inappropriate to classify dead individuals as recovered individuals because the real-world epidemic spread processes show different recovery rates and death rates in different communities. In the present work, a S I R D epidemic model with different recovery rates is proposed. We pay more attention to the changes in the number of dead individuals. The basic reproductive number is obtained. The stationary solutions of a disease-free state and an endemic state are given. We show that quarantining communities can decrease the basic reproductive number, and the total number of dead individuals decreases in a disease-free steady state with an increase in the number of quarantined communities. The most effective quarantining strategy is to preferentially quarantine some communities/cities with a greater population size and a fraction of initially infected individuals. Furthermore, we show that the population flows from a low recovery rate and high population density community/city/country to some high recovery rate and low population density communities/cities/countries, which helps to reduce the total number of dead individuals and prevent the prevalence of epidemics. The numerical simulations on the real-world network and the synthetic network further support our conclusions. [ABSTRACT FROM AUTHOR]

In the absence of effective vaccine/antiviral strategies for reducing the burden of the coronavirus disease 2019 (COVID-19) pandemic in India, the main focus has been on basic non-pharmaceutical interventions (NPIs), such as nationwide lockdown (travel restrictions and the closure of schools, shopping malls, and worshipping and other gathering places), quarantining of exposed individuals, and isolation of infected individuals. In the present study, we propose a compartmental epidemic model incorporating quarantine and isolation compartments to (i) describe the current transmission patterns of COVID-19 in India, (ii) assess the impact of currently implemented NPIs, and (iii) predict the future course of the pandemic with various scenarios of NPIs in India. For R0 < 1, the system has a globally asymptotically stable disease free equilibrium, while for R0 > 1, the system has one unstable disease free equilibrium and a unique locally stable endemic equilibrium. By using the method of least squares and the best fit curve, we estimate the model parameters to calibrate the model with daily new confirmed cases and cumulative confirmed cases in India for the period from May 1, 2020 to June 25, 2020. Our result shows that the implementation of an almost perfect isolation in India and 33.33% increment in contact-tracing on June 26, 2020 may reduce the number of cumulative confirmed cases of COVID-19 in India by around 53.8% at the end of July 2020. Nationwide lockdown with high efficiency can diminish COVID-19 cases drastically, but combined NPIs may accomplish the strongest and most rapid impact on the spreading of COVID-19 in India. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID-19) outbreak, due to SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), originated in Wuhan, China and is now a global pandemic. The unavailability of vaccines, delays in diagnosis of the disease, and lack of proper treatment resources are the leading causes of the rapid spread of COVID-19. The world is now facing a rapid loss of human lives and socioeconomic status. As a mathematical model can provide some real pictures of the disease spread, enabling better prevention measures. In this study, we propose and analyze a mathematical model to describe the COVID-19 pandemic. We have derived the threshold parameter basic reproduction number, and a detailed sensitivity analysis of this most crucial threshold parameter has been performed to determine the most sensitive indices. Finally, the model is applied to describe COVID-19 scenarios in India, the second-largest populated country in the world, and some of its vulnerable states. We also have short-term forecasting of COVID-19, and we have observed that controlling only one model parameter can significantly reduce the disease's vulnerability. [ABSTRACT FROM AUTHOR]

We consider the interacting processes between two diseases on multiplex networks, where each node can be infected by two interacting diseases with general interacting schemes. A discrete-time individual-based probability model is rigorously derived. By the bifurcation analysis of the equilibrium, we analyze the outbreak condition of one disease. The theoretical predictions are in good agreement with discrete-time stochastic simulations on scale-free networks. Furthermore, we discuss the influence of network overlap and dynamical parameters on the epidemic dynamical behaviors. The simulation results show that the network overlap has almost no effect on both epidemic threshold and prevalence. We also find that the epidemic threshold of one disease does not depend on all system parameters. Our method offers an analytical framework for the spreading dynamics of multiple processes in multiplex networks. [ABSTRACT FROM AUTHOR]

The ongoing novel coronavirus epidemic was announced a pandemic by the World Health Organization on March 11, 2020, and the Government of India declared a nationwide lockdown on March 25, 2020 to prevent community transmission of the coronavirus disease (COVID)-19. Due to the absence of specific antivirals or vaccine, mathematical modeling plays an important role in better understanding the disease dynamics and in designing strategies to control the rapidly spreading infectious disease. In our study, we developed a new compartmental model that explains the transmission dynamics of COVID-19. We calibrated our proposed model with daily COVID-19 data for four Indian states, namely, Jharkhand, Gujarat, Andhra Pradesh, and Chandigarh. We study the qualitative properties of the model, including feasible equilibria and their stability with respect to the basic reproduction number R 0. The disease-free equilibrium becomes stable and the endemic equilibrium becomes unstable when the recovery rate of infected individuals increases, but if the disease transmission rate remains higher, then the endemic equilibrium always remains stable. For the estimated model parameters, R 0 > 1 for all four states, which suggests the significant outbreak of COVID-19. Short-time prediction shows the increasing trend of daily and cumulative cases of COVID-19 for the four states of India. [ABSTRACT FROM AUTHOR]

In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed points and stable periodic orbits, as well as regions of bistability. For arbitrary biologically feasible initial population sizes, the probability of evolving toward stable solutions is obtained for each point of the analyzed parameter space. This probability map shows combinations of infection rates of the generalist and specialist strains that might lead to equal chances for each type becoming the dominant strategy. Furthermore, we have identified infection rates for which the model predicts the onset of chaotic dynamics. Several degenerate Bogdanov–Takens and zero-Hopf bifurcations are detected along with generalized Hopf and zero-Hopf bifurcations. This manuscript provides additional insights into the dynamical complexity of host–pathogen evolution toward different infection strategies. [ABSTRACT FROM AUTHOR]