TRANSMISSION DYNAMICS OF HEPATITIS B: ANALY-SIS AND CONTROL

Abstract

The infection of hepatitis B attacks the liver and can produce acute and chronic diseases, while it is a major health problem and life-threatening around the globe. The control of this infection is a difficult task due to several reasons such as variation of human behavior, proper medication, vaccination, and existence of a large number of carries, etc., but understanding the dynamics of the infection helps to design appropriate control strategies. Thus, a proper complex dynamical system is needed to find the stability conditions and propose intervention strategies for forecasting the control of hepatitis B virus transmission. We formulate a model that will be helpful to investigate the temporal dynamics and suggest control strategies for hepatitis B infection. The well-posedness of the proposed model will be shown, and used to find the threshold parameter to analyze the model equilibria and its stability. We also perform the sensitive analysis of the threshold quantity to quantify the most sensitive epidemic parameters. Based on the temporal dynamics and sensitivity, we investigate effective methods to minimize the infection of hepatitis B, and develop the algorithms to support the theoretical results with the help of numerical simulations.

1. INTRODUCTION

Hepatitis means liver inflammation produced by the virus's bacterial infections and continuous exposure to alcohol or drugs (Ganem & Prince, 2004) . Hepatitis B infection is caused by a non-cytopathic virus called the hepatitis B virus (HBV). The viruses are in vaginal fluids, blood, and semen, and are transferred in multiple ways from one individual to other. Major routes of the transmissions are blood, sharing razors, toothbrushes, and unprotected sexual contacts (Chang, 2007) . Another source of HBV transmission is maternal transmission (i.e., from an infected mother to her child). However, this virus can not be transmitted from causal contact (McMahon, 2005) . The infectious hepatitis B has multiple infection phases: acute and chronic carries. The first phase refers to the initial three months after someone becomes infected with hepatitis B. The immune system can recover in this stage without taking any treatment/hospital care usually, however, may also lead to a long-term infection indicating the chronic phase for someone. The individual with chronic HBV stage often has no acute history of infection. The chronic hepatitis B phase is a severe stage and causes many complications, for example, liver scarring, failure of the liver, and liver cancer (Ringehan et al., 2017) . In the chronic hepatitis B phase, there is a need for treatment with medicines, containing oral antiviral agents. The proper treatment and hospital care will be necessary for the rest of their lives, because this can slow cirrhosis progression and reduce the liver cancer incidence with an improvement in long-term survival. In 2021, WHO recommended oral treatments for the hepatitis B virus as the most potent drugs. The symptom of hepatitis B includes skin yellowing, abdominal pain, urine darkness, fever, and loss of appetite, etc. But for every individual, this is not common to suffer from hepatitis B because 40% of the acute individuals have no symptoms in the acute stage of the infection. Although the vaccine for hepatitis B is available, new cases still have been reported and the infection of hepatitis B is one of the main public health issues that produce a high mortality rate around the globe (Shepard et al., 2006) . Worldwide two billion of the population are infected with hepatitis B, among which the number of chronic hepatitis B is 360 million (Libbus & Phillips, 2009) . Viral hepatitis B is a leading source of death among other diseases while producing 820000 deaths in 2019, with 1.5 million newly infected.

