We propose a new deterministic model for the dynamics of malaria and the effectiveness of drugs and the positivity of the model investigated. The human population was portioned into three distinct compartments of susceptible, infected and the recovered, while the mosquito population was portioned into two distinct Compartments of susceptible and the infected, giving rise to a set of five ordinary differential equations. A parameter (A) is introduced to measure the effectiveness of anti malarial drugs in the infected compartment. The dynamics of the model was obtained. It was observed that both the disease free equilibrium states will be stable if () A > 60% and if the mosquitoes population is reduced the human population will also be stable. Numerical simulations were presented to show some results

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In this paper, we introduce a predator-prey with susceptible and infected prey model. The model includes the harvesting of infected prey. We assume that the predator avoids the infected prey. The susceptible prey becomes infected when they are in contact with infected prey and recover to be susceptible again. We find the equilibrium points and the conditions for their existence and stability. We also show the non-existence of periodic solutions. Numerical simulations explain the effect of the parameters on the behaviour of the three classes of populations. The simulations also give the region of the solution and guarantees that all solutions of the system lie within the region.

When the initial state of an epidemic is uncertain, mathematical descriptions of that epidemic in terms of initial conditions must be modified by regarding these initial conditions as random variables having particular distribution functions. In this paper we assume a beta distribution as the initial proportion of infected in an SIR epidemic model. Numerical simulations are carried out on the various classes of the model as the uncertainties are propagated. The probability density functions of the random solutions of these classes over time are also calculated numerically. Some properties of the random solution and the effect of the parameters of the beta distribution on the behaviour of the epidemic are investigated.