Mathematical Modeling of Epidemic and Population Dynamics Systems

Abstract

Epidemiics and population dynamics mathematical modeling is an important instrument of comprehending the dissemination of dreadful diseases, anticipating population changes, and assessing intervention plans. The SIR (Susceptible-Infectious-Recovered), SEIR (Susceptible-Exposed-Infectious-Recovered), and Lotka-Volterra are examples of models used to study the relationship between groups of people and the disease. These models apply the concept of differential equations to the rates of change in populations and disease compartments over time to allow the researcher and the policy makers to predict the peak of an epidemic, assess vaccination policies, and the stability of the population in most cases. Complex dynamics (nonlinearity, stochasticity, and time-dependent intervention) can be studied using mathematical models with the help of computational simulations. This paper provides an overview of the major mathematical models in epidemic and population dynamics modeling, and particularly their uses in the planning of the health of the populace, ecological research and resource management.