Simulation of Mathematical Modeling of Malaria with Vaccination

Objectives

General Objectives. To formulate and analyse malaria with vaccination.

Specific Objectives.

Formulation of malaria model with vaccination.

Estimation of model parameters

Numerical solution

To clarify the importance of vaccination through model parameters discussion.

Methodology: We build a model through a flowchart diagram. We simulate data which helps to find the parameter values that makes the model to fit to the data in order to verify the validity or adequacy of the model.  We use the least squares method to estimate model parameters and interpretation of it. We analyze the model by computing the basic reproduction number R0, the disease-free equilibrium point and endemic point. And also discuss the behavior of numerical solution.  We solve the model numerically using MATLAB software. Numerical solutions of the model are presented in graphical way that allows to visualize the model predictions.

Results: Model has shown that the vaccination rates reduce the basic reproduction number, which means that the vaccination are involved in eradicating malaria from the population. To control the spread of malaria disease, we introduced the herd immunity strategy which is concerned about immunizing a large number of people in population and take protective measures for the rest including children and also pregnancy women. Thus, we calculated the herd immunity threshold which is 0.0517, this value means that 5.17% of susceptible people has to be immunized to control the spread of plasmodium parasite.  Our model was fitted to simulated data which implies that the model can be used to control the transmission of malaria and to predict the mechanism of prevention by vaccination, it has shown that the vaccination strategy involves in eliminating malaria.

Unique contribution: Malaria is an infectious disease that has become very common and is becoming more widespread in an uncontrolled way throughout Africa, as well as the whole world, due to the bite of the female anopheles’ mosquito which spreads the plasmodium. In an attempt to eradicate this deadly disease, a massive response needs to be mounted by governments to enlighten the public about the prevalence of malaria and also provide remedy for treatment of it. On this issue, over the last few decades there have been millions of dollars and much efforts put into the fight against Plasmodium falciparum malaria but unfortunately there is still no registered vaccine against it.  Is the vaccination the best strategy to reduce the number of peoples dying from malaria? Many researchers worked on different model and they did not introduce the vaccination, in my model Introduce the vaccination to see if it is the best strategies to eradicate the number of people dying from malaria