Background
Various mathematical modeling approaches are used to provide a robust framework for understanding the transmission dynamics of infectious diseases in human populations. In an epidemic, models can be used for the analysis of the spread of a disease, forecasting, identifying trends and making parameter estimates which can be used for planning and implementing intervention measures.
Methods
This study utilizes the classical Susceptible - Infected - Recovered (SIR) model to analyze the evolution of COVID-19 in Zambia during the third wave of infections. The model is fitted to actual COVID-19 data for Zambia for the third wave of the pandemic obtained from the Zambia National Public Health Institute (ZNPHI). The transmission and recovery rates are estimated by minimizing the error between the fitted curve and the real data using the least square approach.
Results
Model simulations indicate that the basic reproductive number (\({R}_{0}\)) for Zambia is 1.31 meaning that, on average, 1.31 persons are infected for each infected person. At the worst point of the epidemic, we expect that 591,743 people will contract the virus and 7,144 fatalities will be recorded. To prevent the spread of infection, the model estimates that at least 24 percent of the population will need to be vaccinated. With the country's projected population of about 18.91 million, this translates to roughly 4.5 million people.
Conclusion
The severity of COVID-19 infection, hospitalizations, and deaths in Zambia is substantially higher than national testing data suggests, according to model projections. More modeling work is needed to acquire accurate estimates of the disease burden in society, to inform resource allocation, and to aid mitigation planning, especially in countries that may lack adequate national surveillance systems.
In this paper, we study the optimization problem confronted by an insurance firm whose management can control its cash-balance dynamics by adjusting the underlying premium rate. The firm's objective is to minimize the total deviation of its cash-balance process to some pre-set target levels by selecting an appropriate premium policy. We study the problem in a general framework assuming the state process is governed by a stochastic delay differential equation and the classical utility function being replaced by a recursive utility or stochastic differential utility (SDU). We derive a sufficient maximum principle for an optimal control of such a system and apply the result to discuss some optimal premium rate control problems.
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