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The epidemic growth model is an important tools used in predicting the future of a population and the spread of disease in the population. An epidemic model is usually formed in a differential equation or a system consisting several differential equations. The biological complexity in the underlying population affects the complexity of the epidemic model. One example of biological complexity is the Allee effect which reflects the critical density dependent of the population growth. In this paper we discuss a Logistic epidemic by considering this Allee effect on the population. Dynamic analysis is performed by determining fixed point and its stability analysis in crisp condition. We found the Basic Reproduction Ratio (BRR) for the model. The properties of the solution of the model are explored by the use of its numerical solution. Since we also consider the fuzziness of parameters and variables in the model, the numerical solution is generated using a modified Runge-Kutta method. This is done to explore the effect of inaccuracy and uncertainty which often occur in epidemiological problems.

This paper considers a deterministic model for the transmission dynamics of rabies virus in the wild dogs-human zoonotic cycle. The endemic equilibrium is found and its existence depends on the value of the basic reproduction number. The effect of vaccination in dogs is considered on the model. We then also present the effective reproduction number in the presence of the vaccination. Further we developed the formula to obtain the minimum level of the vaccination to eliminate the endemic equilibrium, which is called the herd vaccination threshold. We found the relation between this herd vaccination threshold and the basic reproduction number. The effect of some fuzzy parameters to the herd vaccination threshold is also investigated.