In this study we propose a Coronavirus Disease 2019 (COVID-19) mathematical model that stratifies infectious subpopulations into: infectious asymptomatic individuals, symptomatic infectious individuals who manifest mild symptoms and symptomatic individuals with severe symptoms. In light of the recent revelation that reinfection by COVID-19 is possible, the proposed model attempt to investigate how reinfection with COVID-19 will alter the future dynamics of the recent unfolding pandemic. Fitting the mathematical model on the Kenya COVID-19 dataset, model parameter values were obtained and used to conduct numerical simulations. Numerical results suggest that reinfection of recovered individuals who have lost their protective immunity will create a large pool of asymptomatic infectious individuals which will ultimately increase symptomatic individuals with mild symptoms and symptomatic individuals with severe symptoms (critically ill) needing urgent medical attention. The model suggests that reinfection with COVID-19 will lead to an increase in cumulative reported deaths. Comparison of the impact of non pharmaceutical interventions on curbing COVID19 proliferation suggests that wearing face masks profoundly reduce COVID-19 prevalence than maintaining social/physical distance. Further, numerical findings reveal that increasing detection rate of asymptomatic cases via contact tracing, testing and isolating them can drastically reduce COVID-19 surge, in particular individuals who are critically ill and require admission into intensive care.

This study considered the modeling of systematic mortality risk for populations with finite data using the Poisson incorporated Credibility regression model. For novelty, we have included the credibility regression approach to modelling mortality by assuming the number of annual deaths follow a Poisson distribution. Our model shows improvement in precision levels when estimating mortality risk compared to classical models used in European countries. We have illustrated that our model works optimally when using Kenyan mortality data, comparing male and female lives under the different strategies, thus making better predictions than the classical Lee–Carter (LC) and Cairns–Blake–Dowd (CBD) models. The mean absolute forecast error (MAFE), mean absolute percentage forecast error (MAPFE), root mean square error (RMSE), and root mean square forecast error (RMSFE) under the incorporated credibility regression model are much lower than the values obtained without incorporation of the Buhlmann credibility approach. The findings of this research will help insurance companies, pension firms, and government agencies in sub-Saharan countries model and forecast systematic mortality risks accurately. Finally, the results are essential in actuarial modelling and pricing, thus making life assurance products affordable for most people in low-income African countries.

We investigate the filtering problem where the borrower’s time varying credit quality process is estimated using continuous time observation process and her (in this paper we refer to the borrower as female and the lender as male) ego-network data. The hidden credit quality is modeled as a hidden Gaussian mean-reverting process whilst the social network is modeled as a continuous time latent space network model. At discrete times, the network data provides unbiased estimates of the current credit state of the borrower and her ego-network. Combining the continuous time observed behavioral data and network information, we provide filter equations for the hidden credit quality and show how the network information reduces information asymmetry between the borrower and the lender. Further, we consider the case when the network information arrival times are random and solve stochastic optimal control problem for a lender having linear quadratic utility function.

Aims/ Objectives: To formulated a linear regression model to capture the relationship between tea production and climatic variables in terms of ARIMA.Place and Duration of Study: Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya, between June 2019 and April 2021.Methodology: The study used time-series data for mean annual temperature, mean annual rainfall, humidity, solar radiation, and NDVI, collected from six counties, namely Embu, Kakamega, Kisii, Kericho, Meru, and Nyeri.Results: The study ndings noted that there is a presence of trend and seasonality for all the data. The scatter plot matrix for all the climatic variables for all the counties under the study indicated that tea production has a linear relationship with most climatic variables. Model t of the data indicated statistical signicance when tea production data is dierenced. A second linear model with tea production data deseasoned has mixed results in terms of a signicancetest. The variation of independent variables with tea production yielded very low values, suggesting that the data used has many variabilities.Conclusion: The study ndings show the climatic variables can be used to forecast tea production.Recommendation: Future studies may combine the analysis with other statistical modeling procedures such as the GARCH models.

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