On Fractional Epidemic Model Order Shigella

Abstract

Introduction: We have adapted the continuous mathematical framework developed to examine the dynamics of a Shigella epidemic at a constant recruitment rate. They divided the population into seven groups in their model: susceptible (S), vaccination(V), exposé(E), infected (I), isolated (G), hospitalized(H) and recovered (R), each with its own set of parameters. We examined a mathematical model of a Shigella outbreak in a community with a constant population using the SVEIGHR compartmental nonlinear deterministic approach. The model was subjected to analytical investigations utilizing the linearized stability method. The greatest eigenvalue of the next-generation matrix yields the fundamental reproductive number , which controls the spread of the disease. The generalized Routh-Hurwitz and Jacobian criterion are used to determine the threshold value . The model is unstable if, , and stable if, . Additionally, we determine the endemic and disease-free equilibrium points, which are helpful for a faster recovery. We have created graphs in Matlab to provide a more accurate model representation.

Objectives: To describe the disease Shigella with the help of SVEIGHER compartmental nonlinear deterministic approach through factorial differential method and compare it to classical differential method and see the results.

Results: From the above studies we conclude that fractional differential method is more effective than classical differential method.

Conclusion : In this paper, we discuss SVEIGHR epidemic  model for disease Shigella . This  SVEIGHR  model controlss the spreading of the disease in Human population. By using Routh-Hurwitz Criteria we find all the eigen values for endemic point are negative which shows that the above model SVEIGHR (Susceptible Vacation Infectious Isolated Hospitalization Recovered) is stable. Extending our work, we can also use harmonic mean type incidence rate for better stability and control the disease.