Sepsis is a life-threatening medical emergency, which is a major cause of death worldwide and the second highest cause of mortality in the United States. Researching the optimal control treatment or intervention strategy on the comprehensive sepsis system is key in reducing mortality. For this purpose, first, this paper improves a complex nonlinear sepsis model proposed in our previous work. Then, bifurcation analyses are conducted for each sepsis subsystem to study the model behaviors under some system parameters. The bifurcation analysis results also further indicate the necessity of control treatment and intervention therapy. If the sepsis system is without adding any control under some parameter and initial system value settings, the system will perform persistent inflammation outcomes as time goes by. Therefore, we develop our complex improved nonlinear sepsis model into a sepsis optimal control model, and then use some effective biomarkers recommended in existing clinic practices as optimization objective function to measure the development of sepsis. Besides that, a Bayesian optimization algorithm by combining Recurrent neural network (RNN-BO algorithm) is introduced to predict the optimal control strategy for the studied sepsis optimal control system. The difference between the RNN-BO algorithm from other optimization algorithms is that once given any new initial system value setting (initial value is associated with the initial conditions of patients), the RNN-BO algorithm is capable of quickly predicting a corresponding time-series optimal control based on the historical optimal control data for any new sepsis patient. To demonstrate the effectiveness and efficiency of the RNN-BO algorithm on solving the optimal control solution on the complex nonlinear sepsis system, some numerical simulations are implemented by comparing with other optimization algorithms in this paper.
\noindent We formulate an age-structured three-staged nonlinear partial differential equation model that features {\it nonlinear} recidivism to the infected ({\it infectious}) class from the {\it temporarily} recovered class. Equilibria are computed, as well as local and global stability of the {\it infection-free} equilibrium. As a result, a backward-bifurcation exists under necessary and sufficient conditions. A generalized numerical framework is established and numerical experiments are explored for two positive solutions to exist in the {\it infectious} class.
The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of many kinds of infectious diseases. In the study of mathematical models of infectious diseases it is important to predict whether the infection disappears or the pathogens persist. The delay kernel is described by the memory function that reflects the influence of the past density of pathogen in the blood. By using the coefficient of kernel k, as a bifurcation parameter, the models are found to undergo a sequence of Hopf bifurcation. The direction and the …
In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all the parameters of the model. Choosing the inverse of latent period as control parameter, over 70% of the interval comprises the coexistence of periodic and chaotic attractors, bistable dynamics. Despite the competition between these attractors, the ch…
We study the dynamics of a SIR epidemic model with nonlinear incidence rate, vertical transmission vaccination for the newborns and the capacity of treatment, that takes into account the limitedness of the medical resources and the efficiency of the supply of available medical resources. Under some conditions we prove the existence of backward bifurcation, the stability and the direction of Hopf bifurcation. We also explore how the mechanism of backward bifurcation affects the control of the infectious disease. Numerical simulations are presented to illustrate the theoretical findings.
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using …
The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that t…
Recent clinical studies have shown that HIV disease pathogenesis can depend strongly on many factors at the time of transmission, including the strength of the initial viral load and the local availability of CD4+ T-cells. In this article, a new within-host model of HIV infection that incorporates the homeostatic proliferation of T-cells is formulated and analyzed. Due to the effects of this biological process, the influence of initial conditions on the proliferation of HIV infection is further elucidated. The identifiability of parameters within the model is investigated and a local stability…
We consider the qualitative behavior of a mathematical model for transmission dynamics with two nonlinear stages of contagion. The proposed model is inspired by phenomena occurring in epidemiology (spread of infectious diseases) or social dynamics (spread of opinions, behaviors, ideas), and described by a compartmental approach. Upon contact with a promoter (contagious individual), a naive (susceptible) person can either become promoter himself or become $\textit{weakened}$, hence more vulnerable. Weakened individuals become contagious when they experience a second contact with members of the …
Mathematical modeling and control of Tuberculosis: Backward and Hopf bifurcations under case-finding and case-holding interventions
Institute of Technological Development for the Chemical Industry (INTEC), CONICET-UNL（化学工业技术开发研究所（INTEC），CONICET-UNL）；Faculty of Chemical Engineering (FIQ) - CONICET-UNL（化学工程学院（FIQ）- CONICET-UNL）；National Institute of Respiratory Diseases (INER)（国家呼吸系统疾病研究所（INER））
We propose a mathematical model to investigate the effects of information-dependent vaccination behavior on meningitis transmission. The information is represented by means of information index as early proposed in (d'Onofrio et al., Theor. pop. biol., 2007). We perform a qualitative analysis based on stability theory, focusing to the global stability of the disease free equilibrium (DFE) and the related transcritical bifurcation taking place at the threshold for the DFE. Finally, we assess the role of epidemiological and information parameters in the model dynamics through numerical simulatio…
A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed nets usage. The occurrence of a backward bifurcation at R_0=1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic reproduction number is less than unity. This phenomenon is found to be caused by disease-induced human mortality. The global asymptotic stability of the endemic equilibrium for R_…
