A mathematical modeling of Hepatitis C Virus (HCV) dynamics has been presented in this paper. The proposed model, which involves four coupled ordinary differential equations, describes the interaction of target cells (hepatocytes), infected cells, infectious virions and non-infectious virions. The model takes into consideration the addition of ribavirin to interferon therapy and explains the dynamics regarding biphasic and triphasic decline of viral load in the model. A critical drug efficiency parameter has been defined and it is shown that for efficiencies above this critical value, HCV is eradicated whereas for efficiencies lower this critical value, a new steady state for infectious virions is reached, which is lower than the previous steady state.

In this article, a nonlinear mathematical model used for the impact of vaccination on the control of infectious disease, Japanese encephalitis with a standard incidence rate of mosquitoes, pigs and humans has been planned and analyzed. During the modeling process, it is expected that the disease spreads only due to get in touch with the susceptible and infected class only. It is also assumed that due to the effect of vaccination, the total human population forms a separate class and avoids contact with the infection. The dynamical behaviors of the system have been explored by using the stability theory of differential equations and numerical simulations. The local and global stability of the system for both equilibrium states under certain conditions has been studied. We have set up a threshold condition in the language of the vaccineinduced reproduction number R(α 1 ), which is fewer than unity, the disease dies in the absence of the infected population, otherwise, the infection remains in the population. Furthermore, it is found that vaccine coverage has a substantial effect on the basic reproduction number. Also, by continuous efforts and effectiveness of vaccine coverage, the disease can be eradicated. It is also found a more sensitive parameter for the transmission of Japanese encephalitis virus by using sensitivity analysis. In addition, numerical results are used to investigate the effect of some parameters happening the control of JE infection, for justification of analytical results.

No abstract

No abstract

Dengue fever is a mosquito-borne infectious disease which is transmitted through Aedes aegypti mosquitoes. It is one of the major global health issues in the tropical and subtropical regions of the world. Its dynamics are very complicated owing to the coupling among multiple transmission pathways and various components in pathogen. Due to absence of proper medicine or vaccination, mathematical modeling plays an important role in understanding the disease dynamics and in designing strategies to control the spread of dengue virus. In this paper, we studied a non-linear vector-host model to investigate the transmission dynamics of dengue virus which can be controlled by vaccination as well as treatment. Analysis of model start with the basic reproduction number $\mathcal R_{0}$, when it is less than one, the system become locally asymptotically stable about the virus-free equilibrium point. We calibrated our proposed model corresponding to transmission of dengue virus using real data for six Indian states, namely Tamil Nadu, Kerala, Delhi, Gujarat, Rajasthan and Karnataka by using the least square method. Moreover, we performed normalized forward sensitivity analysis of the basic reproduction number and obtained that mitigating the disease transmission rate of mosquito and human population is the most important factor in achieving dengue control. Finally, an objective functional has been developed to minimize the cost of the vaccination and solved with the aid of the Pontryagin's Maximum Principle. The implementation of the optimal treatment policy shows a significant reduction of the hospitalized individuals as well as infected individuals. We then performed extensive numerical simulations to validate our theoretical analysis with aid of the estimated model parameters.