Mathematical Analysis of Epidemiological Model of Virus Transmission Dynamics in Perspective of Bangladesh

Abstract

Infectious diseases cause great suffering all over the world like Japan, USA, India, China, Ghana, Bangladesh etc. every year. The cause of infectious diseases are mainly virus and bacteria, they are becoming resistant against existing drugs. Therefore, infectious diseases become great concern in public health. But the spread of infectious disease can be controlled by some preventive steps. To get the control strategy, we have to know the transmission dynamics of the viruses. Mathematical modeling plays a vital role in understanding the transmission dynamics of the virus. In order to find out the control strategy of the infectious diseases, several mathematical models are available in the literatures. SIR and SEIR are the most well-known models regarding the transmission dynamics of the infectious diseases. In this thesis we have applied mathematical model namely SEIR model to realize the dynamics of Influenza A (H1N1) virus and Nipah Virus. By analyzing sensitivity of their disease free equilibrium and endemic equilibrium we have got two controlling strategies –decrease of contact rate and/or increase of recovery rate. Moreover, we have got herd immunity threshold for them by basic reproduction number regarding data of Bangladesh. Our result suggests that vaccinating 15.31% population could be controlled spread out of Influenza A (H1N1) virus and keeping away 77.25% (susceptible) population from close contact with infected people could be controlled outbreak of Nipah virus in Bangladesh at their initial outbreak respectively. Using the above control strategy we have proposed vaccine induced SEIR model for Influenza A (H1N1) virus and controlled induced SEIR model for Nipah virus. For Influenza A (H1N1) virus, we considered 15.31% of the susceptible population will be vaccinated whereas for Nipah virus, 77.25% of the susceptible population will not be in close contact (by awareness) with infected population. Numerical solutions of the proposed vaccine induced SEIR model as well as control induced SEIR model regarding data of Bangladesh reveal the control of the outbreak of both diseases respectively. Moreover numerical simulation have been performed to analyze the performance of SEIR models and proposed control induced SEIR models for both the viruses.