  Let S,I and R be susceptible, infected and recovered populations in a city
affected by an epidemic. The SIR model of Lee, Liu, Tembine, Li and Osher,
\emph{SIAM J. Appl. Math.},~81, 190--207, 2021 of the spatiotemoral spread of
epidemics is considered. This model consists of a system of three nonlinear
coupled parabolic Partial Differential Equations with respect to the space and
time dependent functions S,I and R. For the first time, a Coefficient Inverse
Problem (CIP) for this system is posed. The so-called \textquotedblleft
convexification" numerical method for this inverse problem is constructed. The
presence of the Carleman Weight Function (CWF) in the resulting regularization
functional ensures the global convergence of the gradient descent method of the
minimization of this functional to the true solution of the CIP, as long as the
noise level tends to zero. The CWF is the function, which is used as the weight
in the Carleman estimate for the corresponding Partial Differential Operator.
Numerical studies demonstrate an accurate reconstruction of unknown
coefficients as well as S,I,R functions inside of that city. As a by-product,
uniqueness theorem for this CIP is proven. Since the minimal measured input
data are required, then the proposed methodology has a potential of a
significant decrease of the cost of monitoring of epidemics.
