Emergence of the reproduction matrix in epidemic forecasting.

During the recent COVID-19 pandemic, the instantaneous reproduction number, R(t), has surged as a widely used measure to target public health interventions aiming at curbing the infection rate. In analogy with the basic reproduction number that arises from the linear stability analysis, R(t) is typically interpreted as a threshold parameter that separates exponential growth (R(t) > 1) from exponential decay (R(t) < 1). In real epidemics, however, the finite number of susceptibles, the stratification of the population (e.g. by age or vaccination state), and heterogeneous mixing lead to more complex epidemic courses. In the context of the multidimensional renewal equation, we generalize the scalar R(t) to a reproduction matrix, [Formula: see text], which details the epidemic state of the stratified population, and offers a concise epidemic forecasting scheme. First, the reproduction matrix is computed from the available incidence data (subject to some a priori assumptions), then it is projected into the future by a transfer functional to predict the epidemic course. We demonstrate that this simple scheme allows realistic and accurate epidemic trajectories both in synthetic test cases and with reported incidence data from the COVID-19 pandemic. Accounting for the full heterogeneity and nonlinearity of the infection process, the reproduction matrix improves the prediction of the infection peak. In contrast, the scalar reproduction number overestimates the possibility of sustaining the initial infection rate and leads to an overshoot in the incidence peak. Besides its simplicity, the devised forecasting scheme offers rich flexibility to be generalized to time-dependent mitigation measures, contact rate, infectivity and vaccine protection.

Raha syrup attenuates the morphine withdrawal-induced locomotor sensitisation by increasing the cerebrospinal fluid serotonin in rats receiving the opium tincture maintenance treatment.

Morphine withdrawal increases locomotor sensitisation, relapse and impair regulation of serotonin system. We evaluated the effectiveness of Raha syrup on the cerebrospinal fluid (CSF) serotonin levels following locomotor sensitisation in morphine-withdrawn rats receiving the opium tincture (OT). Morphine withdrawal rats gavaged daily with OT and Raha syrup (for 30 days) and then challenged with morphine and evaluated for locomotor activity and CSF serotonin levels before morphine challenge and 2 weeks after cessation of treatment. Raha syrup attenuated locomotor activity, increased the CSF serotonin after morphine challenge, and continued 2 weeks after cessation of treatment in rats receiving OT. Whereas, rats receiving OT alone after morphine challenge exhibited a relative decrease in locomotor activity, without changing CSF serotonin. Raha syrup attenuated locomotor sensitisation in morphine-withdrawn rats receiving OT probably by increasing serotonin. Therefore, administration of Raha syrup along with OT may benefit to treatment relapse in addicts receiving OT maintenance treatment.