Stochastic models have an important role in modeling and analyzing epidemic diseases for small size population. In this article, we study the generation of stochastic models for epidemic disease susceptible-infective-susceptible model. Here, we use the separation variable method to solve partial differential equation and the new developed modified probability generating function (PGF) of a random process to include a random catastrophe to solve the ordinary differential equations generated from partial differential equation. The results show that the probability function is too sensitive to μ, β and γ parameters.Keywords: epidemic diseases; susceptible-infective-susceptible; deterministic model; stochastic model; probability function 1 Deterministic susceptible-infective-susceptible model Figure shows a deterministic susceptible-infective-susceptible model for an epidemic disease. In this figure, S is the susceptible population, I is the infective population, μ > is the natural death rate, γ > is the removal rate which is a constant. Note that S, I ≥ because they represent the number of people. The infection rate, λ, depends on the number of partners per individual per unit time (r > ) and the transmission probability per partner (β > ). In this system, the first susceptible population in class S is going to be infected, then infected population in class I is going to be susceptible again. The following system of ODE's describes this susceptible-infective-susceptibleFigure illustrates the system (). This system is nonlinear due to the form of λ = βI. Generation stochastic susceptible-infective-susceptible modelIn this section, we present the state of the generation stochastic [-] susceptibleinfective-susceptible model. The stochastic susceptible-infective-susceptible model is similar to the deterministic susceptible-infective-susceptible model, for the deterministic model we can find an exact function but for the stochastic model, we cannot obtain
The proposed two-point one block method has a potential application to solve complicated linear and nonlinear equations of the charged particle confinement in a quadrupole field especially in fine tuning accelerators, and, generally speaking, in physics of high energy.
As we know there are two kind of systems in modeling epidemic disease, deterministic systems and stochastic systems. This two systems relate to deterministic and stochastic epidemic disease models, respectively. Almost we use deterministic model for big population size and stochastic model for small population size. To use stochastic models for epidemic disease models, can obtain good results with less error. Study and solving of full stochastic models has not been yet investigated so more. In this article we use the homotopy analysis method to solve the full stochastic susceptible-infective epidemic disease model in disease-free equilibrium point.
Problem statement: In this study we tried to assess the knowledge of general population (15-45 years), injecting drug users, female sex workers, MSM and male prisoners about HIV prevention in Iran. Approach: Respondents are asked the following set of prompted questions: (a) Can we reduce the risk of HIV transmission by having sex with only one uninfected partner who has no other partners? (b) Can we reduce the risk of getting HIV by using a condom every time we have sex? (c) Can have HIV a healthy-looking person? (d) Can a person get HIV by sharing food with someone who is infected? (e) Can a person get HIV from mosquito bits? Results: In this study at compared with the resent studies we saw that, the general knowledge on the effect of consistent and correct use of condom as means of HIV prevention has been increased. There is a decrease in the number of the youth that assume sting of a mosquito can transmit HIV. There were no remarkable change in the perception of the thought that HIV is not transmitted through eating and the possibility of people living with HIV are safe. Conclusion: The current meta-analysis indicated that the awareness on the positive effect of condomization on HIV prevention has increased in recent years, but it is still far from being satisfactory and other basic knowledge about HIV has not improved and there is still a substantial gap with the desired figures
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