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We present a modification of the alternating iterative method, which was introduced by Kozlov and Maz’ya, for solving the Cauchy problem for the Helmholtz equation in a Lipschitz domain. The reason for this modification is that the standard alternating iterative algorithm does not always converge for the Cauchy problem for the Helmholtz equation. The method is then implemented numerically using the finite difference method. [ABSTRACT FROM PUBLISHER]

Objectives: Mathematical modelling is of interest to study the dynamics of coronavirus disease 2019 (COVID-19), and models such as SEIR (Susceptible-Exposed-Infected-Recovered) have been considered. This article describes the development of a compartmental transmission network model - Susceptible-Exposed-Quarantine-Infectious-Infectious, undetected-Infectious, home-based care-Hospitalized-Vaccinated-Recovered-Dead - to simulate the dynamics of COVID-19 in order to account for specific measures put into place by the Government of Rwanda to prevent further spread of the disease., Methods: The compartments of this model are connected by parameters, some of which are known from the literature, and others are estimated from available data using the least squares method. For the stability of the model, equilibrium points were determined and the basic reproduction number R 0 was studied; R 0 is an indicator for contagiousness., Results: The model showed that secondary infections are generated from the exposed group, the asymptomatic group, the infected (symptomatic) group, the infected (undetected) group, the infected (home-based care) group and the hospitalized group. The formulated model was reliable and fit the data. Furthermore, the estimated R 0 of 2.16 shows that COVID-19 will persist without the application of control measures., Conclusions: This article presents results regarding predicted spread of COVID-19 in Rwanda., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

This paper shows the impact of control measures on the predictive COVID-19 mathematical model in Rwanda through sensitivity analysis of the basic reproduction number R 0 . We have introduced different levels of the control measures in the model, precisely, 90%, 80%, 60%, 40%, 20%, 0% and studied their effects on the variation of the model variables. The results from numerical simulations reveal that the more the adherence to the control measures at the percentage of 90%, 80%, 60%, 40%, 20%, 0%, the more the number of COVID-19 cases, hospitalized and deaths reduces which indicates the reduction of the spread of the pandemic in Rwanda. Moreover, It was shown that the transition rate from the infectious compartment is very sensitive to R 0 as the increase/decrease in its value increases/decreases the value of R 0 and this leads to the high spread or the containment of the pandemic respectively., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors.)