Hybrid neural network models combine the advantages of a neural network's fitting functionality with differential equation models to reflect actual physical processes and are widely used in analyzing time-series data. Most related studies have focused on linear hybrid models, but only a few have examined nonlinear problems. In this work, we use a hybrid nonlinear epidemic neural network as the entry point to study its power in predicting the correct infection function of an epidemic model. To achieve this goal, we combine the bifurcation theory of the nonlinear differential model with the mean-squared error loss and design a novel loss function to ensure model trainability. Furthermore, we find the unique existence conditions supporting ordinary differential equations to estimate the correct infection function. Using the Runge Kutta method, we perform numerical experiments on our proposed model and verify its soundness. We also apply it to real COVID-19 data to accurately discover the change law of its infectivity.
A model of an Ebola epidemic is developed with infected individuals structured according to disease age. The transmission of the infection is tracked by disease age through an initial incubation (exposed) phase, followed by an infectious phase with variable transmission infectiousness. The removal of infected individuals is dependent on disease age, with three types of removal rates: (1) removal due to hospitalization (isolation), (2) removal due to mortality separate from hospitalization, and (3) removal due to recovery separate from hospitalization. The model is applied to the Ebola epidemic…
An actively controlled Susceptible-Infected-Susceptible (actSIS) contagion model is presented for studying epidemic dynamics with continuous-time feedback control of infection rates. Our work is inspired by the observation that epidemics can be controlled through decentralized disease-control strategies such as quarantining, sheltering in place, social distancing, etc., where individuals actively modify their contact rates with others in response to observations of infection levels in the population. Accounting for a time lag in observations and categorizing individuals into distinct sub-popul…
In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment and educational campaign as time-dependent controls functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and the Pontryagin's maximum principle to construct adjoint equations and op…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from animals, and the zoonotic infections always spread on interconnected networks. In this paper, we consider the epidemic spreading on one-way circular-coupled network consist of three interconnected subnetworks. Here, two one-way three-layer circular interactive networks are established by introducing the heterogeneous mean-field approach method, then we get th…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated directly for this model, and the uniformly persistent of the disease and threshold dynamics are obtained. Specially, global dynamics of the model without seasonal force are studied. It is shown that the model has only a disease-free equilibrium which is globally stable if $\mathcal{R}_0\le 1$, and as $\mathcal{R}_0>1$ the disease-free equilibrium is unstabl…
In epidemic modeling, the term infection strength indicates the ratio of infection rate and cure rate. If the infection strength is higher than a certain threshold -- which we define as the epidemic threshold - then the epidemic spreads through the population and persists in the long run. For a single generic graph representing the contact network of the population under consideration, the epidemic threshold turns out to be equal to the inverse of the spectral radius of the contact graph. However, in a real world scenario it is not possible to isolate a population completely: there is always s…
Cities have long served as nucleating centers for human development and advancement. Cities have facilitated the spread of both human creativity and human disease, and at the same time, efforts to minimize the spread of disease have influenced the design of cities. The purpose of this paper is to explore the dynamics of epidemics on networks in order to help design a multi-network city of the future aimed at minimizing the spread of epidemics. In order to do this, we start with the SIR model (susceptible, infected, removed) on a network in which nodes represent cities or regions and edges are …
Different extensions of the classical single-strain SIR model for the host population, motivated by modeling dengue fever epidemiology, have reported a rich dynamic structure including deterministic chaos which was able to explain the large fluctuations of disease incidences. A comparison between the basic two-strain dengue model, which already captures differences between primary and secondary infections, with the four-strain dengue model, that introduces the idea of competition of multiple strains in dengue epidemics shows that the difference between first and secondary infections drives the…
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a $2^n$-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an $n$-dimensional linear time-invariant system, a consequence of which is that the Markov chain is "fast-mixing" when the LTI system is stable, i.e. when $\fracβδ<\frac{1}{λ_{\max}(A)}$ …
We adapt the hybrid mechanistic-statistical approach of Ref. [1] to estimate the total number of undocumented Covid-19 infections in Cuba. This scheme is based on the maximum likelihood estimation of a SIR-like model parameters for the infected population, assuming that the detection process matches a Bernoulli trial. Our estimations show that (a) 60% of the infections were undocumented, (b) the real epidemics behind the data peaked ten days before the reports suggested, and (c) the reproduction number swiftly vanishes after 80 epidemic days.
The susceptible--infected--susceptible (SIS) epidemic process on complex networks can show metastability, resembling an endemic equilibrium. In a general setting, the metastable state may involve a large portion of the network, or it can be localized on small subgraphs of the contact network. Localized infections are not interesting because a true outbreak concerns network--wide invasion of the contact graph rather than localized infection of certain sites within the contact network. Existing approaches to localization phenomenon suffer from a major drawback: they fully rely on the steady--sta…
Understanding the dynamics of computer virus (malware, worm) in cyberspace is an important problem that has attracted a fair amount of attention. Early investigations for this purpose adapted biological epidemic models, and thus inherited the so-called homogeneity assumption that each node is equally connected to others. Later studies relaxed this often-unrealistic homogeneity assumption, but still focused on certain power-law networks. Recently, researchers investigated epidemic models in {\em arbitrary} networks (i.e., no restrictions on network topology). However, all these models only capt…
