Stability Analysis of a Schistosomiasis Transmission Model with Control Strategies

• Main Author: Mouhamadou Diaby
• Format: Article
• Language: English
• Published: Biomath Forum 2015-05-01
• Series: Biomath
• Subjects: Epidemic models; Nonlinear dynamical systems; Monotone systems; Global stability; Reproduction number; Schistosomiasis.
• Online Access: http://www.biomathforum.org/biomath/index.php/biomath/article/view/387

We have established and rigorously analyzed a new mathematical model that describes the dynamics schistosomiasis infection. This model incorporates several realistic features including density-dependent births rate of snails and reduced fecundity in snail hosts. Our qualitative analysis of the deterministic model is made with respect to the stability of the disease free equilibrium and the unique endemic equilibrium. Some biological consequences and control strategies are discussed. We have derived the basic reproduction number above which the infection will be controlled under certain levels. We have shown that the disease free equilibrium is globally asymptotically stable when the basic reproduction number ...