A mathematical model that predicts the number of COVID-19 infections that could occur, going forward, has been developed by a team of modelling experts. 

The team is drawn from Uganda Christian University’s Center for Computational Biology, Makerere University’s Department of Mathematics, the Department of Mathematics and Statistics of Kyambogo University, and the Infectious Diseases Institute, Makerere University. 

The model is intended to help predict the dynamics of COVID-19 within Uganda and inform the next steps following the expiry of the 42-day lockdown period. 

Different scenarios of compliance to Standard Operating Procedures (restrictions), the rate of contact between persons in the community, SARS-CoV-2 testing and vaccination rates have been considered. 

This model is fitted using the monthly data obtained from the Ugandan Ministry of Health COVID-19 daily statistics. The modelling period starts from the date of confirmation of the first case of COVID-19 in Uganda (March 21, 2020) to June 2023. The experts, however, caution that during interpretation of the results, focus should be put on the general trend of the COVID-19 epidemic curve and not necessarily the actual numbers as these are often parameter-sensitive. 

The model projects the number of COVID-19 infections that could occur (prevalence), and those that could be potentially detected by public health systems (the confirmed cases through testing), under the different scenarios.
  
Uganda, like several other countries, continues to grapple with the COVID-19 pandemic. In bid to control the epidemic, the country has largely relied on preventive measures. At the time the first few COVID-19 cases were identified in Uganda (March 2020), the government moved to institute a total lockdown so as to limit the community spread of SARS-CoV-2, the causative agent for COVID-19. 

However, on May 4, 2020, the President of Uganda announced a phased opening of the country, leading to a relaxation of some of the restrictions that had been instituted to limit the spread of SARS-CoV-2. Such restrictions that had contained the first wave of the epidemic included: Suspension of mass gatherings, closure of educational institutions of learning, international travel restrictions, border screenings, restrictions on public and private transport and institution of a nationwide curfew. 

The relaxation was on the understanding that the public would observe standard operating procedures (SOPs) that were instituted by the Ministry of Health. These included maintaining a physical distance, mandatory use of face-masks while in public and ensuring hand hygiene. 

The easing of restrictions, the increasing laxity in observing the SOPs, especially during the Ugandan election period, and the emergence of new SARS-CoV-2 variants have led to a resurgence of the epidemic in the country and have sparked a second wave. As of July 22, 2021, 91,355 confirmed cases and 2,483 deaths had been reported. With just over a million doses of the COVID-19 vaccine administered and increasing positivity rates and case fatalities, it is not surprising that on June 18, 2021, the President declared a second lockdown and a new set of restrictions lasting 42 days. 

This was to try and contain the new wave and protect the already stretched and fragile country’s health system. These measures included suspension of both public and private transport, pulling back of curfew time to 1900hrs-0530hrs from 2100hrs-0530hrs, closure of educational institutions, closure of non-agricultural business centers, re-institution of work-from-home and stay-at-home-orders, except for essential staff and closure of places of worship. 
 
During the lockdown, the government, through the Office of the Prime Minister, has extended financial support to the most vulnerable to cater for basic necessities and ensure their survival. However, with closed businesses and other sources of livelihood, the public remains uncertain of what will happen after the 42 days of lock-down. 

The decisions to lift or extend the lockdown should be well-informed and in position to address pending questions. For example, should the restrictions be extended or lifted and for how long and in what format? By projecting the number of infections that would be observed under different scenarios, models (mathematical, statistical, machine learning algorithms etc.) are useful in assessing the impact of such scenarios so as to arrive at the best course of action. We thus developed a mathematical model to aid in making these important decisions. 
 
Rightly so, the model projects that the current lockdown period will lead to a decrease in the number of infected individuals, as has already been observed. If the lockdown is sustained up to the beginning of October, the epidemic will eventually phase out. However, this may not be feasible and sustainable in the long run. On the other hand, if the current lockdown is lifted and there is low level of adherence to SOPs, the model projects an increase in the number of infected individuals as well as the confirmed cases culminating in a third wave around February 2022. 

The predicted third peak would however be lower compared to what the country has experienced during the second peak. We have also modelled another scenario of medium adherence to SOPs/restrictions after the end of the current lockdown period, given that individuals might be more careful having seen the worst of the second wave of COVID-19. 

In this case, with the same vaccination and testing rates as in the current lockdown period, the numbers of both infected individuals as well as the confirmed cases rise but this time at a relatively slow rate and a third wave is shown to appear later on in November 2022 with a lower peak. 

If we assume an increase in the average number of contacts per month, and a 5-fold increase in testing and vaccination rates after the end of the 42-lockdown period, while maintaining the proportion observing SOPs at medium levels as in the scenario above, the number of infected individuals as well as the confirmed cases will first decrease and then start to increase slowly. A 10-fold increase in testing and vaccination rates leads to a low rise in the number of confirmed cases that eventually goes down. In this case, the infection is controlled. 

The two scenarios namely; increasing the testing and vaccination rates by 5 times and 10 times, show promising results with the 10-fold increase having the same impact of a sustained lockdown.  Increasing the current vaccination rate by 5 times means that by March 2022, 16% of the population of Uganda should have been vaccinated and this proportion would go on to increase to 36% by January 2023. 

On the other hand, increasing the current vaccination rate by 10 times means that by March 2022, 30% of the population of Uganda should have been vaccinated and this proportion would go on to increase to 60% by January 2023. Given the Government’s plan to roll out vaccination to over 21 million Ugandans, this is encouraging. This, therefore, means that the scaling vaccination will ably control the COVID-19 pandemic. 

In as much as lockdown is effective at suppressing the epidemic, lockdown measures are not sustainable in the long run as they negatively impact the economy. The real solution lies in vaccination of a critical mass of individuals known as the herd immunity threshold. 

This is because not all susceptible individuals can be vaccinated due to the scarcity of vaccines while others may shun vaccination programmes due to common antivax theories. It remains important to determine the required proportion of the susceptible individuals that need to be vaccinated for the country to achieve herd immunity. 

In estimating the herd immunity, we derived an expression for the basic reproduction number, a quantity that informs the transmissibility of the virus. With an efficacy of 68% of the AstraZeneca vaccine, the estimated proportion of individuals required to be vaccinated is 75.4% of Uganda’s population which is approximately 33.2 million. 

It is important that the government invests in immunising more Ugandans prior to lifting the current lockdown measures. However, effective control of the COVID-19 pandemic will largely depend on the availability of vaccine doses, reduced testing costs and availability of testing facilities.  

In conclusion, therefore, based on our modelling approaches, the country is likely to experience a third wave early 2022 that will warrant another lockdown, if adequate vaccination is not achieved for more than half of the nation’s population. In addition, vaccination and testing efforts need to be supplemented by a continued sensitization of adherence to the SOPs even after receipt of the vaccine.

The model was developed by Joseph Ssebuliba (PhD), Doreen Mbabazi Ssebuliba (PhD), Juliet Nakakawa Nsumba (PhD), Ronald Galiwango (PhD), Hassan Kayondo (PhD), Henry Kasumba (PhD), Martha Kirabo (MA), Agnes Namyalo (MSc), James Bumba (BSc), Letisha Najjemba (BSc), Bernard Molho Bwambale (BA), Vincent Arumadri (BSc), Agnes Kiragga (PhD) and John Kitayimbwa (PhD).