Mathematical simulation of contagious virus spread

Document Type : Original Article


IT Management, Imam Ali University, Tehran, Iran


In this article we study the prevalence of contagious disease in a community. To this end, we view society as a dynamic system and apply mathematical equations and relationships to it.
First, we present the history of mathematical modeling in the field of contagious diseases and the work done in this field, then find out the probability of the virus spreading in a population with a number of people with contagious disease, and finally the differential equation of disease spread. Obtain the environment and then calculate the time it took to get the disease.
In addition, we also plan to provide a model to describe how a virus is transmitted. In this model, we have four boxes called susceptible individuals, virus carriers, treated individuals, and improved individuals. We obtain the differential equations of growth and decline of each of these boxes and examine the stability condition of the system.


Keeling, M. J., Rohani, P. (2011). Modeling infectious diseases in humans and animals. Princeton University Press.
Padmanabhan, P., Seshaiyer, P., Castillo-Chavez, C. (2017). Mathematical modeling, analysis and simulation of the spread of Zika with influence of sexual transmission and preventive measures. Letters in Biomathematics4(1), 148-166.
Nie, L. F., Xue, Y. N. (2017). The roles of maturation delay and vaccination on the spread of Dengue virus and optimal control. Advances in Difference Equations2017(1), 278.
Khan, M. A., Ali, K., Bonyah, E., Okosun, K. O., Islam, S., Khan, A. (2017). Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control. Scientific reports7(1), 1-19.
Wang, L., Liu, Z., Xu, D., Zhang, X. (2017). Global dynamics and optimal control of an influenza model with vaccination, media coverage and treatment. International Journal of Biomathematics10(05), 1750068.
Khan, T., Zaman, G., Chohan, M. I. (2017). The transmission dynamic and optimal control of acute and chronic hepatitis B. Journal of biological dynamics11(1), 172-189.
Biswas, S., Subramanian, A., ELMojtaba, I. M., Chattopadhyay, J., Sarkar, R. R. (2017). Optimal combinations of control strategies and cost-effective analysis for visceral leishmaniasis disease transmission. PLoS One12(2).
Chowell, G., James, H. (2016). Mathematical and statistical modeling for emerging and re-emerging infectious diseases. 
Rachah, A., Torres, D. F. (2015). Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa. Discrete Dynamics in Nature and Society2015.
Nowzari, C., Preciado, V. M., Pappas, G. J. (2016). Analysis and control of epidemics: A survey of spreading processes on complex networks. IEEE Control Systems Magazine36(1), 26-46.