Development of Mathematical Models for the Analysis of Hepatitis Delta Virus Viral Dynamics

Abstract

BackgroundMathematical models have shown to be extremely helpful in understanding the dynamics of different virus diseases, including hepatitis B. Hepatitis D virus (HDV) is a satellite virus of the hepatitis B virus (HBV). In the liver, production of new HDV virions depends on the presence of HBV. There are two ways in which HDV can occur in an individual: co-infection and super-infection. Co-infection occurs when an individual is simultaneously infected by HBV and HDV, while super-infection occurs in persons with an existing chronic HBV infection.Methodology/Principal FindingsIn this work a mathematical model based on differential equations is proposed for the viral dynamics of the hepatitis D virus (HDV) across different scenarios. This model takes into consideration the knowledge of the biology of the virus and its interaction with the host. In this work we will present the results of a simulation study where two scenarios were considered, co-infection and super-infection, together with different antiviral therapies. Although, in general the predicted course of HDV infection is similar to that observed for HBV, we observe a faster increase in the number of HBV infected cells and viral load. In most tested scenarios, the number of HDV infected cells and viral load values remain below corresponding predicted values for HBV.Conclusions/SignificanceThe simulation study shows that, under the most commonly used and generally accepted therapy approaches for HDV infection, such as lamivudine (LMV) or ribavirine, peggylated alpha-interferon (IFN) or a combination of both, LMV monotherapy and combination therapy of LMV and IFN were predicted to more effectively reduce the HBV and HDV viral loads in the case of super-infection scenarios when compared with the co-infection. In contrast, IFN monotherapy was found to reduce the HDV viral load more efficiently in the case of super-infection while the effect on the HBV viral load was more pronounced during co-infection. The results suggest that there is a need for development of high efficacy therapeutic approaches towards the specific inhibition of HDV replication. These approaches may additionally be directed to the reduction of the half-life of infected cells and life-span of newly produced circulating virions.

Mathematical models of the interrelated dynamics of hepatitis D and B

“…4 shows an example profile whereby both HBV and HDV infections decrease, including free virions. The model of Sousa and Cunha [8] similarly does not predict observed dynamics, with lamivudine effectively reducing both HBV and HDV viral loads.…”

“…(5) and (6) The model structure is similar to other two virus systems [6,8], with the state transitions defined as the possible infection events that can occur. We assume the following transitions are possible:…”

“…Therefore, administration of this drug will result in a reduction of the parameter r at all occurrences. Similar to Sousa and Cunha [8], we introduce the parameter g to represent the efficacy of lamivudine in preventing HBV production.…”

“…The earlier models of Zhang et al [6,7] are related in that they consider the competing dynamics of two viruses in a host plant population. The first known HBV-HDV model was proposed by Sousa and Cunha [8] and investigated numerically. Developing a model of HDV infection in vivo is made difficult by the relative lack of experimental data about the course of infection and the inherent complexity of the system.…”

Integration of Reaction Kinetics Theory and Gene Expression Programming to Infer Reaction Mechanism

“…Mathematical modeling of viral systems such as HIV-1, hepatitis B, and others has been of great interest in the hopes of developing treatment strategies based upon those models (de Sousa and Cunha 2010, Guedj and Neumann 2010, Krishnan 2011, Srivastava et al 2002. Many models of various sizes and structures have been proposed for these systems taking into account a wide range of biochemical species.…”