Although the origins of some diseases that affect humans are not known, many have zoonotic origins (Wolfe et al., 2007). Over the past few decades, there have been several major outbreaks of zoonotic diseases, including influenza, Ebola Virus Disease, SARS/SARS-CoV, MERS-CoV, and COVID-19/SARS-CoV-2. As shown in the Literature section, many researchers have already developed mathematical models that describe the spread of these diseases.

Canada and the United States (US) are major trading partners. The border between Windsor, Ontario and Detroit, Michigan accounts for a significant amount of trade and travel between Canada and the US.

One goal of this project is to present a model for Windsor that accounts for decisions made by city, provincial, and federal governments. Another goal is to develop a user interface that can help public health officials and researchers to make decisions on how to control the spread of these diseases.

Data are provided in the Data namespace (C19M.D.*). Release 4 (R4) of the Health Level 7 Fast Healthcare Interoperability Resources (HL7 FHIR) is used.

In projects in the Models - Compartmental Models - Approximate Solution Methods namespace (C19M.M.C.A.*), approximate solutions for compartmental models are obtained using the ordinary differential equation (ODE) solvers in MathNet.Numerics. Unless otherwise noted, these projects are programmed in C# and use the .NET Framework 4.8.

In projects in the Models - Compartmental Models - System Dynamics namespace (C19M.M.C.SD.*), AnyLogic is used to simulate compartmental models.

March 17, 2020 - "Canada, U.S. working on mutual deal to restrict non-essential travel"

March 18, 2020 - "Canada, U.S. border temporarily closing to non-essential traffic to slow COVID-19"

March 20, 2020 - "CBC Windsor's March 20 COVID-19 update: Windsor declares state of emergency"

March 20, 2020 - "Health unit confirms first case of COVID-19 in Windsor-Essex"

March 21, 2020 - "Michigan healthcare worker living in Windsor-Essex County reported as 2nd local COVID-19 case"

March 26, 2020 - "City of Windsor suspends transit operations starting March 29"

March 28, 2020 - "Canadian nurse working at Detroit hospital: 'We are fighting a war'"

March 31, 2020 - "Ontario-Michigan border dividing line for pandemic that health-care workers cross daily"

April 2, 2020 - "Windsor Regional Hospital to convert St. Clair College SportsPlex into COVID-19 field hospital"

April 5, 2020 - "Detroit-Windsor border officers handing out kits and support as health-care workers travel back and forth"

April 6, 2020 - "Fishing industry in Windsor-Essex shut down during peak season due to COVID-19"

April 8, 2020 - "COVID-19 won’t stop cross-border health care in Windsor"

April 21, 2020 - "Air Canada to temporarily suspend flights to U.S."

April 26, 2020 - "COVID-19 likely spread by building ventilation, say Canadian researchers working on an HVAC fix"

Alexander, M. E., Bowman, C., Moghadas, S. M., Summers, R., Gumel, A. B., & Sahai, B. M. (2004). A vaccination model for transmission dynamics of influenza. SIAM Journal on Applied Dynamical Systems, 3(4), 503-524.

Arino, J., Brauer, F., van den Driessche, P., Watmough, J., & Wu, J. (2006). Simple models for containment of a pandemic. Journal of the Royal Society Interface, 3(8), 453-457.

Chen, T. M., Rui, J., Wang, Q. P., Zhao, Z. Y., Cui, J. A., & Yin, L. (2020). A mathematical model for simulating the phase-based transmissibility of a novel coronavirus. Infectious diseases of poverty, 9(1), 1-8.

Chowell, G., Fenimore, P. W., Castillo-Garsow, M. A., & Castillo-Chavez, C. (2003). SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism. Journal of theoretical biology, 224(1), 1-8.

Gumel, A. B., Ruan, S., Day, T., Watmough, J., Brauer, F., Van den Driessche, P., ... & Wu, J. (2004). Modelling strategies for controlling SARS outbreaks. Proceedings of the Royal Society of London. Series B: Biological Sciences, 271(1554), 2223-2232.

Gumel, A. B., McCluskey, C. C., & Watmough, J. (2006). An SVEIR model for assessing potential impact of an imperfect anti-SARS vaccine.

Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM review, 42(4), 599-653.

Khan, A., & Zaman, G. (2018). Optimal control strategy of SEIR endemic model with continuous age‐structure in the exposed and infectious classes. Optimal Control Applications and Methods, 39(5), 1716-1727.

Lee, J., Chowell, G., & Jung, E. (2016). A dynamic compartmental model for the Middle East respiratory syndrome outbreak in the Republic of Korea: a retrospective analysis on control interventions and superspreading events. Journal of theoretical biology, 408, 118-126.

McLeod, R. G., Brewster, J. F., Gumel, A. B., & Slonowsky, D. A. (2006). Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and outputs. Mathematical Biosciences & Engineering, 3(3), 527.

Ruan, S., Wang, W., & Levin, S. A. (2006). The effect of global travel on the spread of SARS. Mathematical Biosciences & Engineering, 3(1), 205.

Safi, M. A., & Gumel, A. B. (2010). Global asymptotic dynamics of a model for quarantine and isolation. Discrete & Continuous Dynamical Systems-B, 14(1), 209.

Tang, B., Wang, X., Li, Q., Bragazzi, N. L., Tang, S., Xiao, Y., & Wu, J. (2020). Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions. Journal of Clinical Medicine, 9(2), 462.

Thäter, M., Chudej, K., & Pesch, H. J. (2018). Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth. Mathematical Biosciences & Engineering, 15(2), 485.

Wolfe, N. D., Dunavan, C. P., & Diamond, J. (2007). Origins of major human infectious diseases. Nature, 447(7142), 279-283.

Yan, X., & Zou, Y. (2008). Optimal and sub-optimal quarantine and isolation control in SARS epidemics. Mathematical and Computer Modelling, 47(1-2), 235-245.