Nonlinear Infection Rate Research Articles

Stability of In-Host Models of Dengue Virus Transmission with Linear and Nonlinear Infection Rate

Stability of In-Host Models of Dengue Virus Transmission with Linear and Nonlinear Infection Rate

Dynamics of an age-structured HIV model with general nonlinear infection rate

Abstract In this paper, the asymptotical behaviour of an age-structured Human Immunodeficiency Virus infection model with general non-linear infection function and logistic proliferation term is studied. Based on the existence of the equilibria and theory of operator semigroups, linearized stability/instability of the disease-free and endemic equilibria is investigated through the distribution of eigenvalues of the linear operator. Then persistence of the solution semi-flow of the considered system is studied by showing the existence of a global attractor and the obtained result shows that the solution semi-flow is persistent as long as the basic reproduction number $R_{0}>1$. Moreover, the Hopf bifurcations problem around the endemic equilibrium is also considered for the situation with a specific infection function. Since the system has two different delays, four cases are discussed to investigate the influence of the time delays on the dynamics of system around the endemic equilibrium including stability and Hopf bifurcations. At last, some numerical examples with concrete parameters are provided to illustrate the obtained results.

Coupled disease-vaccination behavior dynamic analysis and its application in COVID-19 pandemic

Predicting the evolutionary dynamics of the COVID-19 pandemic is a complex challenge. The complexity increases when the vaccination process dynamic is also considered. In addition, when applying a voluntary vaccination policy, the simultaneous behavioral evolution of individuals who decide whether and when to vaccinate must be included. In this paper, a coupled disease-vaccination behavior dynamic model is introduced to study the coevolution of individual vaccination strategies and infection spreading. We study disease transmission by a mean-field compartment model and introduce a non-linear infection rate that takes into account the simultaneity of interactions. Besides, the evolutionary game theory is used to investigate the contemporary evolution of vaccination strategies. Our findings suggest that sharing information with the entire population about the negative and positive consequences of infection and vaccination is beneficial as it boosts behaviors that can reduce the final epidemic size. Finally, we validate our transmission mechanism on real data from the COVID-19 pandemic in France.

Viral Infection Model with Diffusion and Distributed Delay: Finite-Dimensional Global Attractor.

We study a virus dynamics model with reaction-diffusion, logistic growth terms and a general non-linear infection rate functional response. The model has a distributed delay, including the case of state-selective delay. We construct a dynamical system in a Hilbert space and prove the existence of a finite-dimensional global attractor.

Impact of nonlinear infection rate on HIV/AIDS considering prevalence‐dependent awareness

An HIV/AIDS transmission model is constructed and analyzed that assimilates spontaneous change in human behavior depending on the disease prevalence incorporating self‐shielding mechanism and treatment control. It is assumed that human population become aware of HIV disease from exposed environment and are conscious enough to make their knowledge fruitful by adopting self‐protective measures to reduce disease transmission. We introduce Hill type of behavioral change function and an awareness‐induced transmission function associated with nonlinear infection rate. We emphasize the effectiveness of human awareness in controlling HIV epidemic by investigating the impact of nonlinear incidence rate. Further, an optimal control model is formulated and solved to find the strategy of applying treatment considering spontaneous response of people towards HIV disease. In the numerical simulation segment, impacts of significant parameters have been assessed using sophisticated techniques. We calibrate the proposed model with the real data of HIV cases in India and estimate some crucial model parameters. Moreover, different amalgamations of preventive and treatment controls are introduced. The optimal treatment control has massive impact in curbing HIV epidemic. Also, combined strategy of prevention and treatment can curtail the disease with economic gain. It reveals that effective response of individuals can suppress the disease in such an unexpected situation when treatment rate is low. Increasing the efficacy of human consciousness is much beneficial in curbing HIV outbreak. Thus, our findings highlight a path to control HIV epidemic with uninstructed modification of human behavior by boosting up the productivity of their existing knowledge.

Panic Spreading Model with Different Emotions under Emergency

Emotion plays an important role in decision making. In an emergency, panic can spread among crowds through person-to-person communications and can cause harmful effects on society. The aim of this paper is to propose a new theoretical model in the context of epidemiology to describe the spread of panic under an emergency. First, according to divisions in personality in the context of psychology, groups are divided into a level-headed group and an impatient group. Second, individuals in the two groups have unique personalities. Thus, the level-headed group only infects within the group, while the impatient group considers emotional infection within the group and cross infection between the groups. Then, a nonlinear infection rate is used to describe the probability of infection after an infected person contacts a susceptible person, which is more in line with the real situation. After that, the level-headed group–impatient group nonlinear SIRS panic spreading model is developed. Stable analysis of the model is obtained using the Lyapunov function method to study the stability of the panic-free equilibrium and panic-permanence equilibrium. Finally, simulations are carried out to dynamically describe the spread process of group emotional contagion.

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.

Dynamics of a nonlinear SIQRS computer virus spreading model with two delays

<abstract> In this paper, a Susceptible-Infected-Quarantined-Susceptible (SIQRS) computer virus propagation model with nonlinear infection rate and two-delay is formulated. The local stability of virus-free equilibrium without delay is examined. Furthermore, we also expound and prove that time-delay plays a crucial role in sufficient conditions for the local stability of the virus-existence equilibrium and the occurrence of Hopf bifurcation at the critical value. Especially, direction and stability of the Hopf bifurcation are demonstrated. Finally, some numerical simulations are presented in order to verify the theoretical results. </abstract>

Accounting for multi-delay effects in an HIV-1 infection model with saturated infection rate, recovery and proliferation of host cells

Biological models inherently contain delay. Mathematical analysis of a delay-induced model is, however, more difficult compare to its non-delayed counterpart. Difficulties multiply if the model contains multiple delays. In this paper, we analyze a realistic HIV-1 infection model in the presence and absence of multiple delays. We consider self-proliferation of CD4+T cells, nonlinear saturated infection rate and recovery of infected cells due to incomplete reverse transcription in a basic HIV-1 in-host model and incorporate multiple delays to account for successful viral entry and subsequent virus reproduction from the infected cell. Both of delayed and non-delayed system becomes disease-free if the basic reproduction number is less than unity. In the absence of delays, the infected equilibrium is shown to be locally asymptotically stable under some parametric space and unstable otherwise. The system may show unstable oscillatory behaviour in the presence of either delay even when the non-delayed system is stable. The second delay further enhances the instability of the endemic equilibrium which is otherwise stable in the presence of a single delay. Numerical results are shown to be in agreement with the analytical results and reflect quite realistic dynamics observed in HIV-1 infected individuals.

A viral propagation model with a nonlinear infection rate and free boundaries

In this paper we put forward a viral propagation model with a nonlinear infection rate and free boundaries and investigate the dynamical properties. This model is composed of two ordinary differential equations and one partial differential equation, in which the spatial range of the first equation is the whole space ℝ, and the last two equations have free boundaries. As a new mathematical model, we prove the existence, uniqueness and uniform estimates of the global solution, and provide the criteria for spreading and vanishing, and the long time behavior of the solution components u, v and w. Comparing this model with the corresponding ordinary differential systems, the basic reproduction number $${{\cal R}_0}$$ plays a different role. We find that when $${{\cal R}_0} \le 1$$, the virus cannot spread successfully; when $${{\cal R}_0} > 1$$, the successful spread of virus depends on the initial value and varying parameters.

Impact of farming awareness based roguing, insecticide spraying and optimal control on the dynamics of mosaic disease

Control interventions and farming knowledge are equally important for plant disease control. In this article, a mathematical model has been derived using saturated response functions (nonlinear infection rate) for studying the dynamics of mosaic disease with farming awareness based roguing (removal of infected plants) and insecticide spraying . It is assumed that the use of roguing and spraying depend on the level of awareness about the disease. The model possesses three equilibria namely the trivial, which is always unstable, the disease-free equilibrium which is stable if the basic reproduction number is below unity and the coexisting which may be stable or can exhibit Hopf-bifurcation under certain condition. Finally, we have opted an optimal control problem introducing three control parameters for determining the optimal level of roguing, spraying and cost regarding media awareness for cost-effective control of mosaic disease. Numerical simulations establish the main results suggesting that the awareness campaigns through radio, TV advertisement are important for eradication of the disease. Also, awareness campaign, roguing and spraying should be incorporated with optimal level for cost effective control of mosaic disease.

Modelo para el control óptimo del VIH con tasa de infección dependiente de la densidad del virus

Se propone un modelo en ecuaciones diferenciales ordinarias para describir la dinámica de infección por VIH en una población de células T CD4 susceptibles a la infección y considerando una tasa de infección no lineal densodependiente. Se analiza la estabilidad del modelo con base en el número básico de reproducción, lo que permite determinar resultados de estabilidad y un umbral de control mediante la reducción de la tasa máxima de infección. Luego se formula un problema de control óptimo para establecer funciones óptimas de tratamiento mediante inhibidores de transcriptasa inversa e inhibidores de proteasa, que minimicen la carga viral y los costos directos y/o indirectos de la administración del tratamiento. Se estudian los casos en que la efectividad del tratamiento es nula y plena, y para el caso de efectividad imperfecta del tratamiento se acude al Principio del Máximo de Pontryagin. Se presentan simulaciones numéricas del modelo sin tratamiento y de los diferentes escenarios con tratamiento.

Viral infection model with diffusion and state-dependent delay: Stability of classical solutions

A class of reaction-diffusion virus dynamics models with intracellular state-dependent delay and a general non-linear infection rate functional response is investigated. We are interested in classical solutions with Lipschitz in-time initial functions which are adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions technique is used to analyse stability of interior infection equilibria which describe the cases of a chronic disease.

Global dynamics of a diffusive and delayed viral infection model with cellular infection and nonlinear infection rate

A diffusive and delayed viral dynamics model which incorporates cell-to-cell transmission, cell-mediated immune responses and general nonlinear incidence is investigated. By constructing Lyapunov functionals, it is shown that the global threshold dynamics of the model is fully determined by the basic reproduction numbers of the virus and the immune response, R0 and R1. The result implies that both the basic reproduction number of the virus and the immune response might be underevaluated without considering either the virus-to-cell transmission or cell-to-cell transmission. The main results obtained in this paper extend some known results.

Optimal and Nonlinear Dynamic Countermeasure under a Node-Level Model with Nonlinear Infection Rate

This paper mainly addresses the issue of how to effectively inhibit viral spread by means of dynamic countermeasure. To this end, a controlled node-level model with nonlinear infection and countermeasure rates is established. On this basis, an optimal control problem capturing the dynamic countermeasure is proposed and analyzed. Specifically, the existence of an optimal dynamic countermeasure scheme and the corresponding optimality system are shown theoretically. Finally, some numerical examples are given to illustrate the main results, from which it is found that (1) the proposed optimal strategy can achieve a low level of infections at a low cost and (2) adjusting nonlinear infection and countermeasure rates and tradeoff factor can be conductive to the containment of virus propagation with less cost.

Global Analysis of a Novel Nonlinear Stochastic SIVS Epidemic System with Vaccination Control

This paper proposes a stochastic SIVS epidemic system with nonlinear saturated infection rate under vaccination and investigates the dynamics predicted by the model. By using Itô’s formula and Lyapunov methods, we first study the existence and uniqueness of global positive solution. Then we investigate the stochastic dynamics of the system and obtain the thresholds which govern the extinction and the spread of the epidemic disease. Results show that large stochastic noises can lead to the extinction of epidemic diseases; that is, stochastic disturbances can suppress the outbreak of epidemic diseases. Finally, we carry out a series of numerical simulations to demonstrate the performance of our theoretical findings.

Global Dynamics and Optimal Control of a Viral Infection Model with Generic Nonlinear Infection Rate

This paper is devoted to exploring the combined impact of a generic nonlinear infection rate and infected removable storage media on viral spread. For that purpose, a novel dynamical model with an external compartment is proposed, and the explanations of the main model assumptions (especially the generic nonlinear infection rate) are also examined. The existence and global stability of the unique equilibrium of the model are fully investigated, from which it can be seen that computer virus would persist. On this basis, a next-best approach to controlling the level of infected computers is suggested, and the theoretical analysis of optimal control of the model is also performed. Additionally, some numerical examples are given to illustrate the main results.

Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses

A virus dynamics model with intracellular state-dependent delay and nonlinear infection rate of Beddington-DeAngelis functional response is studied. The technique of Lyapunov functionals is used to analyze stability of an interior infection equilibrium which describes the case of both CTL and antibody immune responses activated. We consider first a particular biologically motivated class of discrete state-dependent delays. Next, the general case is investigated.

Modeling the intracellular pathogen-immune interaction with cure rate

Many common and emergent infectious diseases like Influenza, SARS, Hepatitis, Ebola etc. are caused by viral pathogens. These infections can be controlled or prevented by understanding the dynamics of pathogen-immune interaction in vivo. In this paper, interaction of pathogens with uninfected and infected cells in presence or absence of immune response are considered in four different cases. In the first case, the model considers the saturated nonlinear infection rate and linear cure rate without absorption of pathogens into uninfected cells and without immune response. The next model considers the effect of absorption of pathogens into uninfected cells while all other terms are same as in the first case. The third model incorporates innate immune response, humoral immune response and Cytotoxic T lymphocytes (CTL) mediated immune response with cure rate and without absorption of pathogens into uninfected cells. The last model is an extension of the third model in which the effect of absorption of pathogens into uninfected cells has been considered. Positivity and boundedness of solutions are established to ensure the well-posedness of the problem. It has been found that all the four models have two equilibria, namely, pathogen-free equilibrium point and pathogen-present equilibrium point. In each case, stability analysis of each equilibrium point is investigated. Pathogen-free equilibrium is globally asymptotically stable when basic reproduction number is less or equal to unity. This implies that control or prevention of infection is independent of initial concentration of uninfected cells, infected cells, pathogens and immune responses in the body. The proposed models show that introduction of immune response and cure rate strongly affects the stability behavior of the system. Further, on computing basic reproduction number, it has been found to be minimum for the fourth model vis-a-vis other models. The analytical findings of each model have been exemplified by numerical simulations.

Continuous solutions to a viral infection model with general incidence rate, discrete state-dependent delay, CTL and antibody immune responses

A virus dynamics model with intracellular state-dependent delay and a general nonlinear infection rate functional response is studied. We consider the case of merely continuous solutions which is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functionals technique is used to analyze stability of an interior infection equilibrium which describes the case of both CTL and antibody immune responses activated.