Inventory planning, an important aspect of every industry, is the process of determining the optimal quantity and timing of an organisation’s production and delivery chain in order to ensure that an organization is able to produce and provide its goods and services without resulting in unmet demands due to shortage, or losses due to overstocking. Inventory planning has a different set of challenges in the healthcare and the pharma sector; often characterized by uncertain demand and service times. This problem of resource allocation becomes more complicated due to epidemic diffusion.
Diffusion refers to the process where a variable of interest (e.g. information, disease) spreads from a point of higher concentration to a point of lower concentration. Drawing inspiration from information diffusion in human networks, researchers have attempted to apply the same theoretical principles to explain the spread of epidemics (Woo and Chen, 2016). Epidemic diffusion is a dynamic problem which requires a multivariable approach, especially at the initial stage when we need to consider factors such as nature of the epidemic, the spread and extent of the outbreak. After the onset of any epidemic, researchers, doctors and public officials face critical challenges due to the uncertainty regarding the nature of the epidemic and how it spreads while simultaneously trying to optimize operations to contain the diffusion.
In the past decade, there has been significant research with respect to the modelling and analysis of epidemic diffusion. This research spans from forecasting the outreach of an epidemic (for resource allocation) to the analysis of epidemic diffusion vis-à-vis population migration.
With the emergence new infectious diseases, researchers are directing their efforts to discover trends (by assessment of public health records) in order to deploy necessary preventive measures. Mathematical models of varying complexity and scale such as the time series ARIMA models for short-term forecasting, simple compartmental models which compartmentalize the population into homogenous segments, complex stochastic agent-based modelling which analyses the impact of individual as well as interactive effects of various factors and entities in the system, and metapopulation approaches which consider patterns of diseases in spatially separated populations (and their transitions), are some of the numerous techniques that have been used for forecasting and analysing the outbreak of an epidemic. Although these techniques have proved to be efficient in capturing real-time spread of epidemics, they often require a considerable amount of information which may not necessarily be available in cases of newly emerging infections.
In a series of papers by Liu et al. (2012, 2016, 2020), Ming Liu discusses his research regarding dynamic demand, allocation of medical resources and logistics modelling in the context of real-time epidemic diffusion.
Liu and Zhang (2016) discuss a dynamic logistics model for medical supply distribution during an epidemic. The basic idea of the paper was to create a logistics mechanism wherein the demand for particular medicines during an outbreak is anticipated, in order to optimize the effective cost (by integrating the various components/levels of the supply chain right from the hospitals to the pharmaceutical plants including the in-transit stage). This mechanism is based on a standard compartmental epidemiological model, more specifically the Susceptible-Exposed-Infected-Recovered (SEIR) epidemic diffusion model. This model assumes that an infected person is not quarantined, i.e., can infect a susceptible and exposed individual, and that the people who have recovered will be immune to the infection.
In another paper, Liu et al. (2020) explain two models for optimizing epidemic-logistics networks by leveraging their knowledge of graph theory and mixed integer nonlinear programming models. For the first model, the aim was to optimize emergency material distribution based on the concepts of combinatorial optimization. In simpler terms, they design a multiple-travelling-salesman problem with some modifications, and then use graph theory to optimize the shortest distance / route to be taken for emergency resource allocation. The second model proposes an effective algorithm (using optimization techniques of nonlinear functions) and relationships to enhance location-based allocation of services at the time of an emergency. This aids not just in cost minimization but also in promoting prompt services during disasters in order to enable maximum outreach and a sophisticated, hassle-free execution to contain the spread of the infection.
A suggestion for further research in this area is the implementation of sophisticated machine learning tools like dynamic computational graphs and recurrent neural networks (RNNs). In case of data inadequacy, these models could be used to leverage derivative information like news reports, survey statistics and so on to trace the trajectory, scale and extent of an epidemic. The idea here is to dynamically update the graphs with information as and when received, and further leverage RNNs to extract patterns and make forecasts accordingly.
During biological disasters, it is essential that help reaches people on time – making it absolutely crucial to optimize resource allocation strategies in order to maximize service outreach with minimal delay. Implementing real-time resource allocation methods can help control the number of fatalities due to epidemic diseases.
Deeper research into epidemic diffusion is of crictical importance as we see the the devastating effects of coronavirus play out.
Ameri, K., & Cooper, K. D. (2019). A Network-Based Compartmental Model For The Spread Of Whooping Cough In Nebraska. AMIA Summits on Translational Science Proceedings.
Lega, J., & Brown, H. E. (2016). Data-driven outbreak forecasting with a simple nonlinear growth model. Epidemics, 17, 19-26.
Liu, M., Cao, J., Liang, J., & Chen, M. (2020). Epidemic-Logistics Network Considering Time Windows and Service Level. In Epidemic-logistics Modeling: A New Perspective on Operations Research (pp. 259-280). Springer, Singapore.
Liu, M., & Xiao, Y. (2012). Modeling and analysis of epidemic diffusion within small-world network. Journal of Applied Mathematics.
Liu, M., & Zhang, D. (2016). A dynamic logistics model for medical resources allocation in an epidemic control with demand forecast updating. Journal of the Operational Research Society, 67(6), 841-852. Woo, J., & Chen, H. (2016). Epidemic model for information diffusion in web forums: experiments in marketing exchange and political dialog. SpringerPlus, 5(1), 66.