A model of bi-mode transmission dynamics of hepatitis C with optimal control

Optimal control strategies for the reliable and competitive mathematical analysis of Covid-19 pandemic model

To understand dynamics of the COVID-19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic, and super-spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID-19, reproduction numberR 0 is also computed using next generation matrix method. It is shown that the model is locally stable at disease-free equilibrium point whenR 0 < 1 and unstable forR 0 > 1 . The model has been analyzed for global stability at both of the disease-free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction numberR 0 . A couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.

Non-Invasive Diagnosis of Liver Fibrosis in Chronic Hepatitis C using Mathematical Modeling and Simulation

Hepatitis C is a viral infection (HCV) that causes liver inflammation, and it was found that it affects over 170 million people around the world, with Egypt having the highest rate in the world. Unfortunately, serial liver biopsies, which can be invasive, expensive, risky, and inconvenient to patients, are typically used for the diagnosis of liver fibrosis progression. This study presents the development, validation, and evaluation of a prediction mathematical model for non-invasive diagnosis of liver fibrosis in chronic HCV. The proposed model in this article uses a set of nonlinear ordinary differential equations as its core and divides the population into six groups: Susceptible, Treatment, Responder, Non-Responder, Cured, and Fibrosis. The validation approach involved the implementation of two equivalent simulation models that examine the proposed process from different perspectives. A system dynamics model was developed to understand the nonlinear behavior of the diagnosis process over time. The system dynamics model was then transformed to an equivalent agent-based model to examine the system at the individual level. The numerical analysis and simulation results indicate that the earlier the HCV treatment is implemented, the larger the group of people who will become responders, and less people will develop complications such as fibrosis.

Mathematical modeling of hepatitis c virus (HCV) prevention among people who inject drugs: A review of the literature and insights for elimination strategies

In 2016, the World Health Organization issued global elimination targets for hepatitis C virus (HCV), including an 80% reduction in HCV incidence by 2030. The vast majority of new HCV infections occur among people who inject drugs (PWID), and as such elimination strategies require particular focus on this population. As governments urgently require guidance on how to achieve elimination among PWID, mathematical modeling can provide critical information on the level and targeting of intervention are required. In this paper we review the epidemic modeling literature on HCV transmission and prevention among PWID, highlight main differences in mathematical formulation, and discuss key insights provided by these models in terms of achieving WHO elimination targets among PWID. Overall, the vast majority of modeling studies utilized a deterministic compartmental susceptible-infected-susceptible structure, with select studies utilizing individual-based network transmission models. In general, these studies found that harm reduction alone is unlikely to achieve elimination targets among PWID. However, modeling indicates elimination is achievable in a wide variety of epidemic settings with harm reduction scale-up combined with modest levels of HCV treatment for PWID. Unfortunately, current levels of testing and treatment are generally insufficient to achieve elimination in most settings, and require further scale-up. Additionally, network-based treatment strategies as well as prison-based treatment and harm reduction provision could provide important additional population benefits. Overall, epidemic modeling has and continues to play a critical role in informing HCV elimination strategies worldwide.

On the global stability of an epidemic model of computer viruses

In this paper, we study the global properties of a computer virus propagation model. It is, interesting to note that the classical method of Lyapunov functions combined with the Volterra-Lyapunov matrix properties, can lead to the proof of the endemic global stability of the dynamical model characterizing the spread of computer viruses over the Internet. The analysis and results presented in this paper make building blocks towards a comprehensive study and deeper understanding of the fundamental mechanism in computer virus propagation model. A numerical study of the model is also carried out to investigate the analytical results.

Estimating the Impact of Expanding Treatment Coverage and Allocation Strategies for Chronic Hepatitis C in a Direct Antiviral Agent Era

Hepatitis C virus (HCV) infection is an important worldwide public health problem, and most of the global HCV burden is in low- to middle-income countries. This study aimed to estimate the future burden of chronic hepatitis C (CHC) and the impact of public health policies using novel antiviral agents in Thailand. A mathematical model of CHC transmission dynamics was constructed to examine the disease burden over the next 20 years using different treatment strategies. We compared and evaluated the current treatment (PEGylated interferon and ribavirin) with new treatments using novel direct-acting antiviral agents among various treatment policies. Thailand’s CHC prevalence was estimated to decrease 1.09%–0.19% in 2015–2035. Expanding treatment coverage (i.e., a five-fold increment in treatment accessibility) was estimated to decrease cumulative deaths (33,007 deaths avoided, 25.5% reduction) from CHC-related decompensated cirrhosis and hepatocellular carcinoma (HCC). The yearly incidence of HCC-associated HCV was estimated to decrease from 2,305 to 1,877 cases yearly with expanding treatment coverage. A generalized treatment scenario (i.e., an equal proportional distribution of available treatment to individuals at all disease stages according to the number of cases at each stage) was predicted to further reduce death from HCC (9,170 deaths avoided, 11.3% reduction) and the annual incidence of HCC (i.e., a further decrease from 1,877 to 1,168 cases yearly, 37.7% reduction), but cumulative deaths were predicted to increase (by 3,626 deaths, 3.7% increase). Based on the extensive coverage scenario and the generalized treatment scenario, we estimated near-zero death from decompensated cirrhosis in 2031. In conclusion, CHC-related morbidity and mortality in Thailand are estimated to decrease dramatically over the next 20 years. Treatment coverage and allocation strategies are important factors that affect the future burden of CHC in resource-limited countries like Thailand.

Optimal control analysis of Ebola disease with control strategies of quarantine and vaccination

BACKGROUND

The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world.

METHOD

In this paper, we introduce a deterministic SEIR type model with additional hospitalization, quarantine and vaccination components in order to understand the disease dynamics. Optimal control strategies, both in the case of hospitalization (with and without quarantine) and vaccination are used to predict the possible future outcome in terms of resource utilization for disease control and the effectiveness of vaccination on sick populations. Further, with the help of uncertainty and sensitivity analysis we also have identified the most sensitive parameters which effectively contribute to change the disease dynamics. We have performed mathematical analysis with numerical simulations and optimal control strategies on Ebola virus models.

RESULTS

We used dynamical system tools with numerical simulations and optimal control strategies on our Ebola virus models. The original model, which allowed transmission of Ebola virus via human contact, was extended to include imperfect vaccination and quarantine. After the qualitative analysis of all three forms of Ebola model, numerical techniques, using MATLAB as a platform, were formulated and analyzed in detail. Our simulation results support the claims made in the qualitative section.

CONCLUSION

Our model incorporates an important component of individuals with high risk level with exposure to disease, such as front line health care workers, family members of EVD patients and Individuals involved in burial of deceased EVD patients, rather than the general population in the affected areas. Our analysis suggests that in order for R 0 (i.e., the basic reproduction number) to be less than one, which is the basic requirement for the disease elimination, the transmission rate of isolated individuals should be less than one-fourth of that for non-isolated ones. Our analysis also predicts, we need high levels of medication and hospitalization at the beginning of an epidemic. Further, optimal control analysis of the model suggests the control strategies that may be adopted by public health authorities in order to reduce the impact of epidemics like Ebola.