Investigation on simple modelling Spatio-temporal with mobility for case Covid-19 transmission

One of the factors that influences disease transmission is mobility. The increase in the frequency and reach of infectious disease epidemics is largely due to human mobility in the form of travel between cities and countries. One of the transmission of disease due to mobility is COVID-19. COVID-19 is caused by Coronavirus 2 (SARS-CoV-2) severe acute respiratory syndrome infection. Transmission of this disease can occur through direct contact with infected hosts. This transmission factor plays an important role in determining the occurrence of epidemics in a specific area, and even the transmission of disease in this area is influenced by the surrounding area due to mobility activities. In this study, we focus on discussing the COVID-19 transmission model. First, we discuss systems of time-dependent ordinary differential equations by dividing the population into four compartments: susceptible, exposed, symptomatic infectious, and asymptomatic infectious. The analysis of the model takes the form of determining the basic reproduction number, the existence of equilibrium points, and the stability of each equilibrium point. Sensitivity analysis is also carried out to see the parameters that affect the solution of this model. The transmission rate parameter affects the changes of the susceptible compartment with a negative relationship. Then, sensitivity analysis explains the positive relationship between transmission rate parameter changes and exposed compartments, symptoms, and asymptomatics. This model is modified to a partial differential equation. The effect of mobility, as a diffusion equation, affects the transmission from one region to another. Numerical simulations were given with two different diffusion coefficients, namely 0.0001 and 0.00005. The results showed that the spread of the disease transmission was faster with a diffusion coefficient of 0.0001 compared to 0.00005.