In this article, a mathematical model for hypertensive or diabetic patients open to COVID-19 is considered along with a set of first-order nonlinear differ

This work is related to qualitative behaviour of an epidemic model of pine wilt disease. More precisely, we proved that the reproductive number has sharp threshold properties. It has been shown that how vector population can be reduced by the periodic use of insecticides. Numerical simulations show that epidemic level of infected vectors becomes independent of saturation level by including the transmission through mating.

During the outbreak of an epidemic, it is of immense interest to monitor the effects of containment measures and forecast of outbreak including epidemic peak. To confront the epidemic, a simple SIR model is used to simulate the number of affected patients of coronavirus disease in Romania and Pakistan. The model captures the growth in case onsets, and the estimated results are almost compatible with the actual reported cases. Through the calibration of parameters, forecast for the appearance of new cases in Romania and Pakistan is reported till the end of this year by analysing the current situation. The constant level of number of patients and time to reach this level is also reported through the simulations. The drastic condition is also discussed which may occur if all the preventive restraints are removed.