Lyapunov function and global asymptotic stability for a new multiscale viral dynamics model incorporating the immune system response: Implemented upon HCV.

In this paper, a new mathematical model is formulated that describes the interaction between uninfected cells, infected cells, viruses, intracellular viral RNA, Cytotoxic T-lymphocytes (CTLs), and antibodies. Hence, the model contains certain biological relations that are thought to be key factors driving this interaction which allow us to obtain precise logical conclusions. Therefore, it improves our perception, that would otherwise not be possible, to comprehend the pathogenesis, to interpret clinical data, to control treatment, and to suggest new relations. This model can be used to study viral dynamics in patients for a wide range of infectious diseases like HIV, HPV, HBV, HCV, and Covid-19. Though, analysis of a new multiscale HCV model incorporating the immune system response is considered in detail, the analysis and results can be applied for all other viruses. The model utilizes a transformed multiscale model in the form of ordinary differential equations (ODE) and incorporates into it the interaction of the immune system. The role of CTLs and the role of antibody responses are investigated. The positivity of the solutions is proven, the basic reproduction number is obtained, and the equilibrium points are specified. The stability at the equilibrium points is analyzed based on the Lyapunov invariance principle. By using appropriate Lyapunov functions, the uninfected equilibrium point is proven to be globally asymptotically stable when the reproduction number is less than one and unstable otherwise. Global stability of the infected equilibrium points is considered, and it has been found that each equilibrium point has a specific domain of stability. Stability regions could be overlapped and a bistable equilibria could be found, which means the coexistence of two stable equilibrium points. Hence, the solution converges to one of them depending on the initial conditions.

Dynamical Analysis of a Multiscale Model of Hepatitis C Virus Infection Using a Transformed ODEs Model.

A mathematically identical ordinary differential equations (ODEs) model was derived from a multiscale partial differential equations (PDEs) model of hepatitis c virus infection, which helps to overcome the limitations of the PDE model in clinical data analysis. We have discussed about basic properties of the system and found the basic reproduction number of the system. A condition for the local stability of the uninfected and the infected steady states is presented. The local stability analysis of the model shows that the system is asymptotically stable at the disease-free equilibrium point when the basic reproduction number is less than one. When the basic reproduction number is greater than one endemic equilibrium point exists, and the local stability analysis proves that this point is asymptotically stable. Numerical sensitivity analysis based on model parameters is performed and therefore the result describes the influence of each parameter on the basic reproduction number.

How accurate is the diagnosis of rheumatic fever in Egypt? Data from the national rheumatic heart disease prevention and control program (2006-2018).

Rheumatic heart disease (RHD) as a chronic sequela of repeated episodes of acute rheumatic fever (ARF), remains a cause of cardiac morbidity in Egypt although it is given full attention through a national RHD prevention and control program. The present report reviews our experience with subjects presenting with ARF or its sequelae in a single RHD centre and describes the disease pattern over the last decade. A cross-sectional study was conducted in El-Mahalla RHD centre between 2006 and 2018. A total of 17014 individual were enrolled and evaluated. Diagnosis ARF was based on the 2015 revised Jones criteria and RHD was ruled in by echocardiography. The majority of the screened subjects were female (63.2%), in the age group 5-15 years (64.6%), rural residents (61.2%), had primary education (43.0%), and of low socioeconomic standard (50.2%). The total percentage of cases presenting with ARF sequelae was 29.3% [carditis/RHD (10.8%), rheumatic arthritis (Rh.A) (14.9%), and Sydenham's chorea (0.05%)]. Noticeably, 72% were free of any cardiac insult, of which 37.7% were victims of misdiagnoses made elsewhere by untrained practitioners who prescribed for them long term injectable long-acting penicillin [Benzathine Penicillin G (BPG)] without need. About 54% of the study cohort reported the occurrence of recurrent attacks of tonsillitis of which 65.2% underwent tonsillectomy. Among those who experienced tonsillectomy and/or received BPG in the past, 14.5% and 22.3% respectively had eventually developed RHD. Screening of family members of some RHD cases who needed cardiac surgery revealed 20.7% with undiagnosed ARF sequalae [RHD (56.0%) and Rh.A (52.2%)]. Upon the follow-up of RHD cases, 1.2% had improved, 98.4% were stable and 0.4% had their heart condition deteriorated. Misdiagnosis of ARF or its sequelae and poor compliance with BPG use may affect efforts being exerted to curtail the disease. Updating national guidelines, capacity building, and reliance on appropriate investigations should be emphasized. Since the genetic basis of RHD is literally confirmed, a family history of RHD warrants screening of all family members for early detection of the disease.