Mathematical models for devising the optimal Ebola virus disease eradication

A drug-disease model for predicting survival in an Ebola outbreak

REGN-EB3 (Inmazeb) is a cocktail of three human monoclonal antibodies approved for treatment of Ebola infection. This paper describes development of a mathematical model linking REGN-EB3's inhibition of Ebola virus to survival in a non-human primate (NHP) model, and translational scaling to predict survival in humans. Pharmacokinetic/pharmacodynamic data from single- and multiple-dose REGN-EB3 studies in infected rhesus macaques were incorporated. Using discrete indirect response models, the antiviral mechanism of action was used as a forcing function to drive the reversal of key Ebola disease hallmarks over time, for example, liver and kidney damage (elevated alanine [ALT] and aspartate aminotransferases [AST], blood urea nitrogen [BUN], and creatinine), and hemorrhage (decreased platelet count). A composite disease characteristic function was introduced to describe disease severity and integrated with the ordinary differential equations estimating the time course of clinical biomarkers. Model simulation results appropriately represented the concentration-dependence of the magnitude and time course of Ebola infection (viral and pathophysiological), including time course of viral load, ALT and AST elevations, platelet count, creatinine, and BUN. The model estimated the observed survival rate in rhesus macaques and the dose of REGN-EB3 required for saturation of the pharmacodynamic effects of viral inhibition, reversal of Ebola pathophysiology, and survival. The model also predicted survival in clinical trials with appropriate scaling to humans. This mathematical investigation demonstrates that drug-disease modeling can be an important translational tool to integrate preclinical data from an NHP model recapitulating disease progression to guide future translation of preclinical data to clinical study design.

A multicompartment mathematical model to study the dynamic behaviour of COVID-19 using vaccination as control parameter

To analyse novel coronavirus disease (COVID-19) transmission in India, this article provides an extended SEIR multicompartment model using vaccination as a control parameter. The model considers eight classes of infection: susceptible ( S ), vaccinated ( V ), exposed ( E ), asymptomatic infected ( A ), symptomatic infected ( I ), isolated ( J ), hospitalised ( H ), recovered ( R ). To begin, a mathematical study is performed to demonstrate the suggested model's uniform boundedness, epidemic equilibrium, and basic reproduction number. The findings indicate that if,R 0 < 1 , the disease-free equilibrium is locally asymptotically stable; but, if,R 0 > 1 the equilibrium is unstable. Secondly, we examine the effect on those who have received vaccinations with what are deemed optimal values. The suggested model is numerically simulated using MATLAB 14.0, and the results confirm the capacity of the proposed model to provide an accurate forecast of the progress of the epidemic in India. Finally, we examine the impact of immunisation on COVID-19 dissemination.

Nanotechnology-based antiviral therapeutics

The host immune system is highly compromised in case of viral infections and relapses are very common. The capacity of the virus to destroy the host cell by liberating its own DNA or RNA and replicating inside the host cell poses challenges in the development of antiviral therapeutics. In recent years, many new technologies have been explored for diagnosis, prevention, and treatment of viral infections. Nanotechnology has emerged as one of the most promising technologies on account of its ability to deal with viral diseases in an effective manner, addressing the limitations of traditional antiviral medicines. It has not only helped us to overcome problems related to solubility and toxicity of drugs, but also imparted unique properties to drugs, which in turn has increased their potency and selectivity toward viral cells against the host cells. The initial part of the paper focuses on some important proteins of influenza, Ebola, HIV, herpes, Zika, dengue, and corona virus and those of the host cells important for their entry and replication into the host cells. This is followed by different types of nanomaterials which have served as delivery vehicles for the antiviral drugs. It includes various lipid-based, polymer-based, lipid-polymer hybrid-based, carbon-based, inorganic metal-based, surface-modified, and stimuli-sensitive nanomaterials and their application in antiviral therapeutics. The authors also highlight newer promising treatment approaches like nanotraps, nanorobots, nanobubbles, nanofibers, nanodiamonds, nanovaccines, and mathematical modeling for the future. The paper has been updated with the recent developments in nanotechnology-based approaches in view of the ongoing pandemic of COVID-19.Graphical abstract.

Mathematical Modeling for Prediction Dynamics of the Coronavirus Disease 2019 (COVID-19) Pandemic, Quarantine Control Measures

A mathematical model for forecasting the transmission of the COVID-19 outbreak is proposed to investigate the effects of quarantined and hospitalized individuals. We analyze the proposed model by considering the existence and the positivity of the solution. Then, the basic reproduction number (R0)—the expected number of secondary cases produced by a single infection in a completely susceptible population—is computed by using the next-generation matrix to carry out the stability of disease-free equilibrium and endemic equilibrium. The results show that the disease-free equilibrium is locally asymptotically stable if R0<1, and the endemic equilibrium is locally asymptotically stable if R0>1. Numerical simulations of the proposed model are illustrated. The sensitivity of the model parameters is considered in order to control the spread by intervention strategies. Numerical results confirm that the model is suitable for the outbreak that occurred in Thailand.

Effect of sexual transmission on the West Africa Ebola outbreak in 2014: a mathematical modelling study

The outbreak of the Ebola virus has resulted in significant morbidity and mortality in the affected areas, and Ebola virus RNA has been found in the semen of the survivors after 9 months of symptom onset. However, the role that sexual transmission played in the transmission is not very clear. In this paper, we developed a compartmental model for Ebola virus disease (EVD) dynamics, which includes three different infectious routes: contact with the infectious, contact with dead bodies, and transmission by sexual behaviour with convalescent survivors. We fitted the model to daily cumulative cases from the first reported infected case to October 25, 2014 for the epidemic in Sierra Leone, Liberia and Guinea. The basic reproduction numbers in these countries were estimated as 1.6726 (95%CI:1.5922–1.7573), 1.8162 (95%CI:1.7660–1.8329) and 1.4873 (95%CI:1.4770–1.4990), respectively. We calculated the contribution of sexual transmission to the basic reproduction number R₀ as 0.1155 (6.9%), 0.0236 (2.8%) and 0.0546 (3.7%) in Sierra Leone, Liberia and Guinea, respectively. Sensitivity analysis shows that the transmission rates caused by contacts with alive patients and sexual activities with convalescent patients have stronger impacts on the R₀. These results suggest that isolating the infectious individuals and advising the recovery men to avoid sexual intercourse are efficient ways for the eradication of endemic EVD.

Replacement, Refinement, and Reduction in Animal Studies With Biohazardous Agents

Animal models are critical to the advancement of our knowledge of infectious disease pathogenesis, diagnostics, therapeutics, and prevention strategies. The use of animal models requires thoughtful consideration for their well-being, as infections can significantly impact the general health of an animal and impair their welfare. Application of the 3Rs—replacement, refinement, and reduction—to animal models using biohazardous agents can improve the scientific merit and animal welfare. Replacement of animal models can use in vitro techniques such as cell culture systems, mathematical models, and engineered tissues or invertebrate animal hosts such as amoeba, worms, fruit flies, and cockroaches. Refinements can use a variety of techniques to more closely monitor the course of disease. These include the use of biomarkers, body temperature, behavioral observations, and clinical scoring systems. Reduction is possible using advanced technologies such as in vivo telemetry and imaging, allowing longitudinal assessment of animals during the course of disease. While there is no single method to universally replace, refine, or reduce animal models, the alternatives and techniques discussed are broadly applicable and they should be considered when infectious disease animal models are developed.