Mathematical Analysis of Control Strategies of HCV in a Community with Inflow of Infected Immigrants

Neterindwa Ainea^1*, Estomih S. Massawe¹, Oluwole Daniel Makinde², Lucy Namkinga³

¹Mathematics Department, University of Dar es Salaam, Dar es Salaam, Tanzania.
²Faculty of Military Science, Stellenbosch University, Cape Town, South Africa.
³Department of Molecular Biology and Biotechnology, University of Dar es Salaam, Dar es Salaam, Tanzania.

DOI: 10.4236/aid.2015.51001                

Abstract

In this paper, we derive and analyse rigorously a mathematical model of control strategies (screening, education, health care and immunization) of HCV in a community with inflow of infected immigrants. Both qualitative and quantitative analysis of the model is performed with respect to stability of the disease free and endemic equilibria. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Using Lyapunov method, endemic equilibrium is globally stable under certain conditions. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the HCV model in a community with inflow of infected immigrants. However, analysis shows that screening, education, health care and immunization have the effect of reducing the transmission of the disease in the community.

Keywords

HCV Disease, Infected Immigrants, Stability, Sensitivity Index, Lyapunov Method, Screening, Education, Health Care and Immunization

Conflicts of Interest

The authors declare no conflicts of interest.

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