The problem is just too ill-defined to fit directly with a logistic model or really any general-purpose model (such as gbm, etc). You need better priors, either

The problem is just too ill-defined to fit directly with a logistic model or really any general-purpose model (such as gbm, etc). You need better priors, either in the form of good, specified dynamics, or in other terms. You could do a regularized stratified model [0], for example, in the case where you have plenty of data in one country but not in others, or similar cases which incorporate dynamics (log-log models of growth are also pretty good). Overall, I think it's just too hard of a problem as it is very ill-posed—even if we knew the exact dynamics, any small perturbation in the data samples significantly changes the best fit (in other words, the dynamics of the system are 'chaotic'). ----- [0] https://stanford.edu/~boyd/papers/pdf/eigen_strat.pdf https://stanford.edu/~boyd/papers/pdf/eigen_strat.pdf