General Incidence Rate Research Articles

Global stability analysis for a SEI model with nonlinear incidence rate and asymptomatic infectious state

In this paper, we propose a generalized SEI epidemic model with a general nonlinear incidence rate and death rate functions. Furthermore, we consider that those who spread the disease are the infected and the exposed. Applying the direct Lyapunov method, we prove that the endemic equilibrium is globally asymptotically stable when the basic reproduction number R0 is greater than unity and the disease free equilibrium is globally asymptotically stable when R0 is lower than unity. We conclude that in order to obtain global stability and uniqueness of the equilibrium points, monoticity is necessary but not differentiability in the functions present in the model.

Global properties of an age-structured virus model with saturated antibody-immune response, multi-target cells, and general incidence rate

Some viruses, such as human immunodeficiency virus, can infect several types of cell populations. The age of infection can also affect the dynamics of infected cells and production of viral particles. In this work, we study a virus model with infection-age and different types of target cells which takes into account the saturation effect in antibody immune response and a general non-linear infection rate. We construct suitable Lyapunov functionals to show that the global dynamics of the model is completely determined by two critical values: the basic reproduction number of virus and the reproductive number of antibody response.

A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate

Abstract This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g ( S ) I . We introduce the generalized stochastic threshold R s ( g ) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when R s ( g ) = 1 . Numerical illustrations of the findings are given via different types of function g .

Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis

In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number R_{0} is less than unity and unstable when R_{0} > 1. The analysis shows that the phenomenon of backward bifurcation occurs when R_{0}<1. Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.

Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response

In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium E*0, CTL-inactivated infection equilibrium E*1 and CTL-activated infection equilibrium E*2. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters R0 and R1, if R0 ≤ 1, E*0 is globally asymptotically stable, if R1 ≤ 1 R0, E*1 is globally asymptotically stable and if R1 >1, E*2 is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at E*2 changes completely, although R1 > 1, a Hopf bifurcation at E*2 is established. In the end, we present some numerical simulations.

Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity

&lt;abstract&gt;&lt;p&gt;In this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of the SEIQ epidemic model. Furthermore, a stationary distribution for the model is obtained and the ergodic holds by using the method of Khasminskii. Finally, the theoretical results are verified by some numerical simulations. The simulation results show that the noise intensity has a strong influence on the epidemic spreading.&lt;/p&gt;&lt;/abstract&gt;

Global stability of a delayed and diffusive virus model with nonlinear infection function

This paper studies a delayed viral infection model with diffusion and a general incidence rate. A discrete-time model was derived by applying nonstandard finite difference scheme. The positivity and boundedness of solutions are presented. We established the global stability of equilibria in terms of by applying Lyapunov method. The results showed that if is less than 1, then the infection-free equilibrium is globally asymptotically stable. If is greater than 1, then the infection equilibrium is globally asymptotically stable. Numerical experiments are carried out to illustrate the theoretical results.

Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate

We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response and the memory effect is described by the Caputo fractional derivative. Stability and instability of equilibrium points are determined in terms of the basic reproduction number. Furthermore, a fractional optimal control system is formulated and the best strategy for minimizing the spread of the disease into the population is determined through numerical simulations based on the derived necessary optimality conditions.

Stability and bifurcation analysis of an HIV-1 infection model with a general incidence and CTL immune response

In this paper, with eclipse stage in consideration, we propose an HIV-1 infection model with a general incidence rate and CTL immune response. We first study the existence and local stability of equilibria, which is characterized by the basic infection reproduction number and the basic immunity reproduction number . The local stability analysis indicates the occurrence of transcritical bifurcations of equilibria. We confirm the bifurcations at the disease-free equilibrium and the infected immune-free equilibrium with transmission rate and the decay rate of CTLs as bifurcation parameters, respectively. Then we apply the approach of Lyapunov functions to establish the global stability of the equilibria, which is determined by the two basic reproduction numbers. These theoretical results are supported with numerical simulations. Moreover, we also identify the high sensitivity parameters by carrying out the sensitivity analysis of the two basic reproduction numbers to the model parameters.

ESTIMATING WHITE NOISE INTENSITY REGIONS FOR COMPARABLE PROPERTIES OF A CLASS OF SEIRS STOCHASTIC AND DETERMINISTIC EPIDEMIC MODELS

<abstract> A comparative stochastic and deterministic study of a family of epidemic models for vector-borne diseases e.g. malaria and dengue fever etc. is presented. The family type is determined by a general nonlinear incidence rate of the disease. Two major sources of environmental white noises are considered: disease transmission and natural death rates. The impacts of each source of noise on the disease dynamics are examined. The basic reproduction numbers and other threshold values for the disease in the stochastic and deterministic settings are determined and compared to determine the impacts of the noises on the dynamics. The question about the extend that stability conditions for steady states in the noise-free disease dynamics, remain valid for the stochastic stability of the steady state is answered in this paper. Moreover, noise intensity regions are computed, within which all stability conditions for both systems are the same, and both systems behave similarly. </abstract>

Crank-Nicholson difference scheme for the system of nonlinear parabolic equations observing epidemic models with general nonlinear incidence rate.

In this work, we study second order Crank-Nicholson difference scheme (DS) for the approximate solution of problem (1). The existence and uniqueness of the theorem on a bounded solution of Crank-Nicholson DS uniformly with respect to time step τ is proved. In practice, theoretical results are presented on four systems of nonlinear parabolic equations to explain how it works on one and multidimensional problems. Numerical results are provided.

Stochastic dynamical probes in a triple delayed SICR model with general incidence rate and immunization strategies

Disease transmission play prominent role in the course of infection dynamics in any epidemic outbreak. A mathematical probe on the stochastic dynamics of SICR model structure with generalized incidence rate and three time delays forms the crux of this article. With Lyapunov theory, the existence of unique positive global solution, and the predictable lanes for both the extinction and persistence of disease in the community have been explored. Also, we exemplify the existence of unique ergodic stationary distribution in the system. Theoretical establishments are supplemented with numerical substantiations to depict real dynamics.

On analysis and optimal control of a SEIRI epidemic model with general incidence rate

This paper deals with the study of a SEIRI epidemic model with relapse and general incidence function. Using the next-generation matrix method, we have looked for the expression of the basic reproduction rate R0 and analyzed the equilibria’s existence and local stability. More precisely, we have established that the two equilibrium points are locally asymptotically stables. In addition, we have used three control functions to control the evolution of the proposed model. We have determined the optimal control by means of the Pontryagin’s maximum principle. Also, some numerical simulations are given to illustrate the theoretical results.

Effect of breastfeeding on the development of infection-related diseases during hospitalization in late preterm infants in 25 hospitals in Beijing, China

OBJECTIVE To investigate the incidence rate of infectious diseases during hospitalization in late preterm infants in Beijing, China, as well as the risk factors for infectious diseases and the effect of breastfeeding on the development of infectious diseases. METHODS Related data were collected from the late preterm infants who were hospitalized in the neonatal wards of 25 hospitals in Beijing, China, from October 23, 2015 to October 30, 2017. According to the feeding pattern, they were divided into a breastfeeding group and a formula feeding group. The two groups were compared in terms of general status and incidence rate of infectious diseases. A multivariate logistic regression analysis was used to investigate the risk factors for infectious diseases. RESULTS A total of 1 576 late preterm infants were enrolled, with 153 infants in the breastfeeding group and 1 423 in the formula feeding group. Of all infants, 484 (30.71%) experienced infectious diseases. The breastfeeding group had a significantly lower incidence rate of infectious diseases than the formula feeding group (22.88% vs 31.55%, P=0.033). The multivariate logistic regression analysis showed that breastfeeding was an independent protective factor against infectious diseases (OR=0.534, P=0.004), while male sex, premature rupture of membranes, gestational diabetes mellitus, and asphyxia were risk factors for infectious diseases (OR=1.328, 5.386, 1.535, and 2.353 respectively, P < 0.05). CONCLUSIONS Breastfeeding can significantly reduce the incidence of infectious diseases and is a protective factor against infectious diseases in late preterm infants. Breastfeeding should therefore be actively promoted for late preterm infants during hospitalization.

Prenatal diethylstilbestrol exposure and risk of diabetes, gallbladder disease, and pancreatic disorders and malignancies.

Prenatal diethylstilbestrol (DES) exposure is associated with increased risk of hormonally mediated cancers and other medical conditions. We evaluated the association between DES and risk of pancreatic cancer and pancreatic disorders, type 2 diabetes, and gallbladder disease, which may be involved with this malignancy. Our analyses used follow-up data from the US National Cancer Institute DES Combined Cohort Study. Cox proportional hazards models estimated hazard ratios (HRs) and 95% confidence intervals (CIs) adjusted for age, sex, cohort, body mass index, smoking, and alcohol for the association between prenatal DES exposure and type 2 diabetes, gallbladder disease (mainly cholelithiasis), pancreatic disorders (mainly pancreatitis), and pancreatic cancer among 5667 exposed and 3315 unexposed individuals followed from 1990 to 2017. Standardized incidence rate (SIR) ratios for pancreatic cancer were based on age-, race-, and calendar year-specific general population cancer incidence rates. In women and men combined, the hazards for total pancreatic disorders and pancreatitis were greater in the prenatally DES exposed than the unexposed (HR = 11, 95% CI 2.6–51 and HR = 7.0, 95% CI 1.5–33, respectively). DES was not associated overall with gallbladder disease (HR = 1.2, 95% CI 0.88–1.5) or diabetes (HR = 1.1, 95% CI 0.9–1.2). In women, but not in men, DES exposure was associated with increased risk of pancreatic cancer compared with the unexposed (HR: 4.1, 95% CI 0.84–20) or general population (SIR: 1.9, 95% CI 1.0–3.2). Prenatal DES exposure may increase the risk of pancreatic disorders, including pancreatitis in women and men. The data suggested elevated pancreatic cancer risk in DES-exposed women, but not in exposed men.

Second Tumors in Pediatric Patients Treated with Double-Scattered Proton Therapy

We hypothesize that double-scattered proton therapy results in neutron dissemination far beyond the treatment field, resulting in an increased risk of second malignancies that disproportionally affect pediatric patients. Between 2006 and 2019, 1708 consecutive children ≤ 21 years old were treated with double-scattered proton therapy at a single institution. Most common indications included CNS tumors (60%), sarcomas (28%), and head/neck tumors (5%). The median age at treatment was 9.2 years, and 370 children were ≤ 3 years. Thirty-five patients (2%) had tumor predisposition syndromes: 18 with neurofibromatosis (NF), 11 with retinoblastoma, and 6 with Li-Fraumeni (LF). Across the cohort, the median prescription dose was 54 Gy (range, 15 - 75.6 Gy). The median follow-up duration was 3.5 years (range, 0.1 - 12.8 years) and includes 6886 total person-years in follow-up. Four hundred patients have ≥ 5 years of follow-up. Seven patients (0.4%) were lost to follow-up. A second tumor was defined as any solid neoplasm throughout the body. The Kaplan-Meier product limit method estimated freedom from second tumor and the log-rank test statistic estimated the level of statistical significance between strata of patients with tumor predisposition syndromes and those patients without. Standardized incidence ratio (SIR) was assessed as the ratio of the observed/expected cases for second solid tumor development using general pediatric incidence rates from the Surveillance, Epidemiology, and End Results (SEER) Program. Seven patients overall developed second tumors resulting in a 5- and 10-year cumulative incidence of 0.4% (95% CI: 0.1-1.1%) and 1.9% (95% CI: 0.8%-4.4%), respectively. The SIR was 7.9. All patients who developed second tumors were irradiated at ≤ 5 years old. There was a statistically significant correlation between patients with NF or LF and second tumors (p < 0.0001). Excluding these patients, 5- and 10-year rates were 0.2% (95% CI: 0-1.1%) and 1.1% (95% CI: 0.4- 3.6%), respectively, and no second tumors developed in regions receiving < 50 Gy. Two patients overall developed hematologic second malignancies < 12 months following chemotherapy and radiation. Second tumors are rare within the decade following double-scattered proton therapy, particularly among children irradiated at > 5 years of age and those without tumor predisposition syndrome. Longer follow-up is needed to empirically validate claims that proton therapy results in less overall second tumors in children, but it is unlikely that neutrons from double-scattered proton therapy in children result in an increased rate of “out-of-field” second tumors.

Mittag-Leffler stability and bifurcation of a nonlinear fractional model with relapse

In this paper, we propose to study a fractional-order SIRI epidemic model with relapse and a general non-linear incidence rate. The existence of solutions, steady states and sufficient conditions to ensure the asymptotic stability are investigated. Meanwhile, a complete analysis of the global stability as well as the stability in the sense of Mittag-Leffler is provided. Indeed, we showed that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R0 is less or equal to unity. However, it is Mittag-Leffler stable only if R0<1. In addition, the positive equilibrium is shown to be globally asymptotically stable whenever R0>1, but it is not stable in the sense of Mittag-Leffler. An estimate of the rate of convergence is derived for every initial condition. In the second part of this work, we incorporated a time delay into the proposed model to describe the period preceding the relapse. By considering the delay as a bifurcation parameter, it was shown that the system undergoes a Hopf-bifurcation when the delay passes through a critical value τ0 leading to the appearance of limit cycles. Our findings, reveal that the combination of fractional order derivative and time delay enriches the behaviors and increase the complexity of the model. By means of the modified Adams–Bashforth–Moulton predictor–corrector scheme, numerical simulations are implemented to support and illustrate the theoretical results.

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching.

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm the results established along this paper.

Spatial dynamics and optimization method for a network propagation model in a shifting environment

<p style='text-indent:20px;'>In this paper, a reaction-diffusion <inline-formula><tex-math id="M1">\begin{document}$ ISCT $\end{document}</tex-math></inline-formula> rumor propagation model with general incidence rate is proposed in a spatially heterogeneous environment. We first summarize the well-posedness of global solutions. Then the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> is introduced for the model which contains the spatial homogeneity as a special case. The threshold-type dynamics are also established in terms of <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>, including the global asymptotic stability of the rumor-free steady state and the uniform persistence of all positive solutions. Furthermore, by applying a controller to this model, we investigate the optimal control problem. Employing the operator semigroup theory, we prove the existence, uniqueness and some estimates of the positive strong solution to the controlled system. Subsequently, the existence of the optimal control strategy is established with the aid of minimal sequence techniques and the first order necessary optimality conditions for the optimal control is deduced. Finally, some numerical simulations are performed to validate the main analysis. The results of our study can theoretically promote the regulation of rumor propagation on the Internet.

A time-delayed SVEIR model for imperfect vaccine with a generalized nonmonotone incidence and application to measles

In this paper, we investigate the effects of the latent period on the dynamics of infectious disease with an imperfect vaccine. We assume a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population when the number of infectious individuals increases. After we propose the model, we provide the well-posedness property by verifying the non-negativity and boundedness of the models solutions. Then, we calculate the effective reproduction number RE. The threshold dynamics of the system is obtained with respect to RE. We discuss the global stability of the disease-free equilibrium when RE<1 and explore the system persistence when RE>1. Moreover, we prove the coexistence of an endemic equilibrium when the system persists. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to: (i) implement a case study regarding the measles disease transmission in the United States from 1963 to 2016; (ii) study the local and global sensitivity of RE with respect to the model parameters; (iii) discuss the stability of endemic equilibrium; and (iv) explore the sensitivity of the proposed model solutions with respect to the main parameters.