A student pilot learns how to fly using a model plane before he or she is qualified to fly a real one.
They are required to navigate through all possible scenarios that could possibly arise like the loss of one engine, crosswind conditions, turbulence and loss of altitude. These they learn through flying a model plane in a simulated environment.
Pandemics, just like flying, are complex, which makes experimental or observational studies difficult. But, mathematical models can help. These kind of models use mathematical concepts to describe a real-world system and are governed by specific rules and assumptions.
When fitted to clinical data, these models prove to be extremely helpful in understanding disease dynamics. Hence, mathematical modellers attempt to understand the transmission dynamics of various pandemics and predict the most effective controls in slowing down the disease spread.
In 1902, Sir Ronald Ross received a Nobel Prize in Medicine and Physiology when he pioneered the use of mathematical modelling in pandemic studies and confirmed that mosquitoes are the vectors responsible for malaria transmission.
My research at the University of Nairobi centred on constructing mathematical models to understand the impact of comprehensive knowledge, HIV/Aids testing, condom use and antiretroviral therapy on the transmission dynamics of this killer disease among adolescents in Kenya.
The model results suggests protecting susceptible adolescent girls and young women against new HIV/Aids infection requires increasing adolescent boys and young men’s knowledge of the disease, and vice versa. The Universal Test and Treat strategy by the World Health Organization requires that all those testing for HIV/Aids be initiated into antiretroviral therapy (ART) immediately to achieve 90 per cent diagnosis of all HIV positive individuals. Of those HIV positively diagnosed, 90 per cent need to be initiated into ART in order to achieve 90 per cent viral load suppression.
The model simulations further revealed that even with all these, the youth population who are not aware of their HIV/Aids status may still be a hindrance to the HIV/Aids war.
Today, Covid-19 has the world’s attention. Mathematical modelling is useful in predicting various scenarios regarding the transmission dynamics of Covid-19. Many Kenyans are now familiar with contact tracing and social distancing, as these terms are often used in press briefings. We could use mathematical models to understand the impact of contact tracing or social distancing in the transmission dynamics.
Mathematical models could also come in handy in understanding the impact of relaxing lockdown measures. For instance, mathematical modelling researchers at the University of Johannesburg, South Africa, found that relaxing social distancing in South Africa by two per cent could result in increasing the cumulative cases by 23 per cent whereas increasing the levels of social distancing by two per cent could bring down cumulative cases by 18 per cent.
Mathematical model formulations could also help in determining the number of secondary infections arising from one infected case. It is estimated that every person infected with Covid-19 will transmit it to three people. With different age groups and pre-existing conditions like diabetes, these estimates could change.
Flattening the Covid-19 curve will be possible if its reproduction number falls below unity.
To contain pandemics, populations need to achieve herd immunity, which is realised when a large percentage acquire immunity either through previous infections or vaccination. Mathematical models are useful in understanding the percentage of a given population that needs to be vaccinated to achieve herd immunity or the number of those that need to recover from the infection before herd immunity kicks in.
The initial phase of an epidemic requires collaborative efforts of various disciplines. It will be critical to employ mathematical modelling tools in Kenya before relaxing lockdown measures.
Marilyn Ronoh is a PhD Student, Applied Mathematics, University of Nairobi