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In this research, we conducted an analysis using a stochastic neural network (SNN) approach to explore the dynamics of Ebola virus disease. Ebola virus, commonly referred to as Ebola hemorrhagic fever, is initially transmitted to humans through contact with wild and domesticated animals. Subsequently, it spreads rapidly among individuals through person-to-person transmission. To control the spread of the Ebola virus, we employed a five-compartmental mathematical model comprising the following classes: susceptible ($S$), exposed ($E$), infected ($I$), quarantined ($Q$) and recovered ($R$). We utilized the aforementioned SNN method for this purpose. The primary aim of this study is two-fold: first, to assess the convergence and accuracy of our proposed method, and second, to elucidate the impact of Ebola disease control measures. Lastly, we conducted a comparative analysis of our findings with those obtained from the numerical solvers ode15s and ode23e, demonstrating the precision and efficacy of our technique in addressing the current disease challenge.

In this paper, we have formulated a compartmental epidemic model with exponentially decaying transmission rates to understand the Ebola transmission dynamics and study the impact of control measures to basic public health. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. We have calculated the basic reproduction number through next generation matrix and investigated the spatial spread of the epidemic via reaction–diffusion modeling. Instead of fitting the model to the observed pattern of spread, we have used previously estimated parameter values and examined the efficacy of predictions of the designed model vis-à-vis the pattern of spread observed in Sierra Leone, West Africa. Further, we conducted a sensitivity analysis to determine the extent to which improvement in predictions is achievable through better parameterization.

We performed numerical simulations with and without control measure for the designed model system. A significant reduction in infection and death cases were observed when proper control measures are incorporated in the model system. Two-dimensional simulation experiments show that infectious population and the number of deaths will increase up to one and a half years without control, but it will decline after two years. We have reported the numerical results, and it closely matches with the real situation in Sierra Leone.

In this paper, a mathematical model of Ebola virus with contact tracing as a control strategy was developed and analyzed. We considered the model without contact tracing and with perfect contact tracing. The two sub-models have been explicitly analyzed. In the first sub-model, it has been found that the disease-free equilibrium (DFE) is both locally and globally asymptotically stable whenever the associated control reproduction number is less than one. The endemic equilibrium point (EEP) is globally asymptotically stable whenever the associated control reproduction number is greater than one. In the second sub-model, it has been found that the DFE is both locally and globally asymptotically stable whenever the control reproduction number is less than one. The EEP is globally asymptotically stable whenever the control reproduction number is greater than one. The full model has also been analyzed, which shows that the DFE is both locally and globally asymptotically stable whenever the associated control reproduction number is less than one. The EEP is globally asymptotically stable whenever the control reproduction number is greater than one. In sensitivity analysis part, effective contact rate for humans was very sensitive in increasing the basic reproduction number and personal hygiene was very sensitive in decreasing the basic reproduction number also, numerical simulation shows that the Ebola virus can be wiped out in society if contact tracing and personal hygiene can be implemented perfectly in the human population.

In this research, the goal is to formulate a mathematical model that predicts the transference mechanisms of Ebola virus (EBOV) and Nipah virus (NIV) infections. They utilize fractional-order derivatives to describe the behavior of the viruses, particularly focusing on the difference in disease manifestation between humans and fruit bats, the putative natural reservoirs. Additionally, they employ fixed-point theory to analyze the qualitative aspects of their model. Also, we investigate the stability of the model using Ulam-Hyers-type results. Furthermore, we utilize the fractional Atangana–Baleanu integral and the Adams–Milton numerical method using MATLAB to provide graphical representations and insights into the behavior of the viruses under various conditions of transference.

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In this paper, we study a fractional-order model with time-delay to describe the dynamics of Ebola virus infection with cytotoxic T-lymphocyte (CTL) response in vivo. The time-delay is introduced in the CTL response term to represent time required to stimulate the immune system. Based on fractional Laplace transform, some conditions on stability and Hopf bifurcation are derived for the model. The analysis shows that the fractional-order with time-delay can effectively enrich the dynamics and strengthen the stability condition of fractional-order infection model. Finally, the derived theoretical results are justified by some numerical simulations.

A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population, infected with Ebola virus, on human-to-human transmission of Ebola Virus Disease (EVD) in a disease-free area. In view of the dynamics of Ebola virus disease, here, the infected class is supposed to be divided into subclasses, viz. primary and secondary infected. The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation. The obtained results, qualitatively and quantitatively, suggest that migration and contact rates play an important role in controlling the spreading of disease. Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values, it leads to delay in the stabilization of the system. It is also found that primary reproductive number increases with increase in migration rate. Besides this, the approximate time required to attain stability of the disease model system is also determined. The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.