The authors have declared that no competing interests exist.

Cameroon is battling against the novel coronavirus (COVID-19) pandemic. Although several control measures have been implemented, the epidemic continues to progress. This paper analyses the evolution of the pandemic in Cameroon and attempts to provide insight on the evolution of COVID-19 within the country’s population.

A susceptible-infected-recovered-dead (SIRD)-like model coupled with a discrete time-dependent Markov chain was applied to predict COVID-19 distribution and assess the risk of death. Two main assumptions were examined in a 10-state and 3-state Markov chain: i) a recovered person can get infected again; ii) the person will remain recovered. The COVID-19 data collected in Cameroon during the period of March 6 to July 30, 2020 were used in the analysis.

COVID-19 epidemic showed several peaks. The reproductive number was 3.08 between May 18 and May 31; 2.75 between June 1 and June 25, and 2.84 between June 16 and June 24. The number of infected individuals ranged from 17632 to 26424 (June 1 to June 15), and 28100 to 36628 (June 16 to June 24). The month of January 2021 was estimated as the last epidemic peak. Under the assumption that a recovered person will get infected again with probability 0.15, 50000 iterations of the Markov chain (10 and 3- state) demonstrated that the death state was the most probable state. The estimated lethality rate was 0.44, 95%CI=0.10%-0.79%. Mean lethality rate assuming ii) was 0.10. Computation of transition probabilities from reported data revealed a significant increase in the number of active cases throughout July and August, 2020, with a mean lethality rate of 3% by September 2020.

Multiple approaches to data analysis is a fundamental step for managing and controlling COVID-19 in Cameroon. The rate of transmission of COVID-19 is growing fast because of insufficient implementation of public health measures. While the epidemic is spreading, assessment of major factors that contribute to COVID-19-associated mortality may provide the country’s public health system with strategies to reduce the burden of the disease. The model outputs present the threatening nature of the disease and its consequences. Considering the model outputs and taking concrete actions may enhance the implementation of current public health intervention strategies in Cameroon. Strict application of preventive measures, such as wearing masks and social distancing, could be reinforced before and after the opening of learning institutions (schools and universities) in the 2020/2021 calendar year and next.

As the novel coronavirus continues to race around the world at a frightening and ferocious pace, governments, organizations, and many research institutes are searching for ways to safeguard lives and effectively fight against the pandemic

Several methodological approaches have been applied to describe disease trends and identify priorities in public health interventions. Among these approaches, compartment models have been widely used during the early stage of the COVID-19 pandemic to attempt to understand its transmission dynamics

The contribution of deterministic models in the fight against COVID-19 pandemic has enabled the development of strategies to slow down the burden of the disease

Several parameters are necessary to build the transition probability of the burden of COVID-19 and its trends: the probability of an active case to recover, the probability that an active case dies, and the probability that a recovered person remains cured or gets re-infected. An active case is defined as a COVID-19-infected individual who can be with or without mild or moderate symptoms, or in a severe or critical condition. On the other hand, there is a probability of re-infection after recovering

In this study, we present the current trend of COVID-19 in Cameroon and estimate the number of infected Cameroonian individuals using a differential equation model (a susceptible-infected-recovered-dead (SIRD) model) based on cumulative confirmed cases. The evolution of the disease (susceptibility, infection, recovery, death) was first modelled using a ten-state Markov chain, followed by a three-state Markov chain. The risk of death was estimated by a simulated Markov chain from transition probability-based modelling. The aim of the present study was to model the epidemic curve and promote preventive measures against COVID-19.

Daily records of the COVID-19 cases were obtained from a public repository (

By July 30, the total number of cases reported were 17255, among whom 391, 15320, and 1544 died, recovered, or remained active cases, respectively, bringing the cure rate to 88.8% and a lethality rate to 2.3%. However, the number of cases started increasing from July 7 to 30, with regular increase of confirmed cases, suggesting the continuity of the epidemic. Data showed a constant increase of confirmed cases with a short period of under-reporting of cases. Under-reporting was noted during the month of July. A slight increase in the number of deaths was observed in July 19 (

Active cases can be either symptomatic with mild, severe, or critical disease condition, or asymptomatic. Cabore

Two approaches were adopted: a SIRD model, and a discrete-time Markov chain with different transition probabilities.

The first modelling experiment used the data from May 18 to May 31 (two weeks before the end of lockdown) to project the epidemic trend in June, July and August. The second modelling experiment used the data from June 1 to June 24 to project the trend of the pandemic in July and August 2020. The risk of an increased number of deaths was assessed using data from March 6 to June 24, 2020. Some modelling experiments like the transition probabilities were calculated on aggregated data over time (from March 6 to July 30, 2020) since individual data were not available and were used to estimate the total number of infected persons during the month of July 2020.

The SIRD model was used, first, to examine the evolution of the epidemic during the last two weeks in May (throughout the period of May 18 to June 24), and, secondly, during the whole month of June after the first re-opening of learning institutions to end the 2019/2020 academic year, with the purpose of assessing the impact of learners on the epidemic trends, and to predict the trend of the epidemic in Cameroon

Details regarding the model are found in the appendices, equation A.1, as well the calculation of R0

Given a day and an infected individual, there are different intra-individual status and circumstances of disease transmission. An infected individual can become a closed case (i.e., death), or recovered/discharged, or remain an active case (who is not yet completely recovered and not dead). An active case can have either mild symptoms or serious/critical condition that could either lead to death or recovery. We assumed that a recovered individual could get infected again if re-exposed to the virus.

We were interested in estimating the transition probability among different possible states and the probability of death given the other conditions. The state of death was regarded as an absorbent state since an individual cannot leave that state once he or she is classified as dead. Active case and recovered states were assumed to be transient as individuals can leave these states and return to them after some time. These multiple states occur as a random process usually known as a stochastic process.

We applied a Markov chain with multiple states (3 and 10) to estimate the probability of the death state to occur, and the probability of death number to increase. It is known that Markov chain property states that, the probability of an event to occur in the future, given the past and the present conditions, depends only on the present condition

In this paper, 1 denotes the active case, 2 the recovery state, and 3 the death state. It was assumed that a recovered individual is still at risk of being re-infected. Therefore, possible transitions are represented by the following sequences: 1 1, 1 2, 1 3, 2 1. Discrete Markov chain models assume that the current state of observation fully depends on the state of the observations at the previous time step per discrete time interval. Mathematically, this means that the probability to observe state

There is evidence to suggest that, among symptomatic cases, the probability of having mild, moderate, severe, or critical disease is approximately 40%, 40%, 15% and 5%, respectively (Epidemiology group, Park M). Hospitalisation rates vary depending on hospitalisation policy and capacity in a given region or country, but it is estimated that 30% of symptomatic patients need hospitalisation, with the highest case fatality rate (CFR) in critical cases (up to 89% without intervention) and 49% for severely ill patients

Cabore

Since an infected person can be classified into one of the enumerated disease conditions with probability 0.8, 0.08, 0.08, 0.03, 0.01, for asymptomatic, mild, moderate, severe, and critical states, respectively

The estimate of RoE in Cameroon accounted for several factors, such as the sanitation and hygiene practice, gathering events, re-opening of learning institution, and other factors of vulnerabilities (Cabore

The Markov chain and the probabilities of all transition states are illustrated in

On the left:10-state disease with one absorbent state (death), with the assumption that a recovered person can get infected again. On the right: three-state transitioning probabilities built from the 10-states. This figure was built using the R package

To assess whether the epidemic curve will continue to increase, we studied the number of active cases/recovered/death from March 6 to June 24. The trend was viewed as a time series, and each section of the data was classified into 3 categories: “increase”, “drop”, or “constant” over time, starting from March 6 to June 24. The decomposition yielded a sequence of three states from which a first order Markov chain was fitted to obtain a transition probability between increase, drop and constant states

A 3-state Markov model was applied on the data during the period starting from March 6 to July 30, 2020to study the evolution of the disease, to assess the impact of control measures recommended by the Cameroonian government, and to estimate the total number of cases of COVID-19 in Cameroon. Yang Liu (2020) provided a comprehensive set of formula to derive the transition probabilities for COVID-19 using a 3-state Markov chain such that, as time

Given the assumptions and statistical data, we used several innovative methods embedded in the R Epidemics Consortium (RECON) suite tools in R (

Two weeks before learning institutions re-opened, i.e. from May 18 to May 31, 2020 (a time period characterized by the relaxation of measures initially imposed by the government to the population at the onset of the pandemic in Cameroon), the SIRD model estimated a basic reproduction number R0 of 3.08, and a social distancing effect of 0.50.

Before the peak of the epidemic that occurred on June 15, R0 was estimated as 2.75, with α = 0.479, implying a small decrease compared to two weeks later. This decrease could be due to the total number of reported infected cases that remained constant for more than four days. The estimated number of infected individuals ranged from 17632 to 26424 (median=21587) persons.

From June 16 to June 24, the model estimated R0 as 2.84 (α=0.45), which yielded the number of infected individuals ranging from 28100 to 36628, suggesting the continuity of the disease severity. Projection of COVID-19 cases revealed an increase rate throughout the month of August (

There was an absence of reporting between June 25 and July 6, 2020. The projected cases (June 1 to July 30) was made by adding the total observed cases between June 25 and July 30, to June1-June 24 data. The model projected an increase in the number of death by mid-August 2020. The dotted dark-green curve and the orange dashed line provide the interval of the epidemic evolution in Cameroon by Mid-August 2020.

A long-term projection based on the data from May 1 to June 24, 2020 shows an exponential epidemic trend by mid-August 2020 (

The consequence of this increase in the number of infected individuals could inevitably lead to an increase in the number of deaths. The projection during the month of May and June showed that the mortality rate associated with Covid-19 was increasing rapidly (

Using a homogeneous Markov chain with ten-state disease (

Assessment of the future occurring state using the ten-state Markov chain 50000 iterations of a chain was ran and the probability of attaining each state was calculated using different initial states (asymptomatic, exposed, infected, mild, and moderate); all except asymptomatic condition constantly led to death state as the most likely.

Given the assumption that a recovered person can be re-infected, the transition matrix on

On the other hand, assuming that a recovered person will remain uninfected (which is in agreement with the country data on June 24), i.e. p11=0.0896, p12=0.8878, and p13= 0.0226, after a run of 50000 iterations and 25000 first iterations discarded, the recovered state was the most probable outcome. Estimates of the lethality rate yielded 2.4% with a 95% confidence interval (CI) of 2.45-2.53.

The transition probabilities p11=0.2, p12=0.72, p13=0.08, p21=0.15, and p22=0.85 defined in

After discretizing each reported time series data (from March 6 to June 24) into several sub-time series data showing either a decrease, an increase, or constant values, we looked at the probability of having an increased number of active cases, recovered cases, and deaths over the months of July, August and September 2020. Indeed, for each COVID-19 data (active case, recovered or death), a 3 - dimensional discrete Markov Chain was built using the sequence generated by the following states: “constant”, “drop”, and “increase. For each sequence, we were interested in the increasing probability. The simulation carried out over 92 days starting from June 24 revealed an increase in the number of deaths throughout August and September (

The computed transition probabilities from March 6 to July 30, 2020 yielded a mean of p11=0.33, p12=0.65, and p13=0.02. These transition probabilities are graphically shown in appendix B (

Legend: the transition probabilities were computed from the time series of reported COVID-19 cases. The projected number of total cases was significantly higher than the observed total cases. It was expected more than 24000 cases by July 30, 2020.

This study used several comprehensive analytical options to model the trend of COVID-19 epidemic in Cameroon. The analysis was first performed using the compartment model to predict COVID-19 morbidity, followed by the application of Markov chain transition probabilities with different assumptions.

The basic reproductive number obtained by the first method was significantly greater than 2.37 as reported by Musa SS et al.

Increase in the mortality rate associated with COVID-19 epidemic raises questions on several aspects related to the main causes of death due to COVID-19. It is known that old age, males, and the presence of chronic comorbidities are associated with more severe disease and higher mortality

This analysis implicitly showed that, severe COVID-19 cases may still be present and had been partially quantified using mass screening tests during the month of July. Despite that fact, the number of active cases remained constant during almost 2 weeks, from June 25 to July 6.

Studies to ascertain the number of COVID-19 cases being identified suggest the SARS-CoV-2 ascertainment rate of 2.22–35.58%, indicating that many non-severe cases are not included in reported cases

The data analysed in the present study lacked individual demographic and patient clinical data. Indeed, modelling experiments presented here did not include some vital factors such as the youthfulness of the population, immunomodulation related to permanent contact with certain infectious agents and/or vaccines, cross-reactive immunity between SARS-CoV-2 and other strains of coronaviruses, the widespread use of antimalarial drugs, zinc, vitamin C, and other complementary therapies that may be responsible of actual reduce infections and mortality in Cameroon and many African countries if compared to other countries in Europe and United State of America.

Future models should account for the number of hospitalized patients under treatment and information on how they evolve from one disease stage to another during hospitalization for the purpose of evaluating the benefit of the treatment.

Strict implementation of self-protection and possible protective measures such as wearing a mask and staying indoor to reduce the risk of getting infected, should continue to be applied by the population to avoid future outbreaks. In addition, the public should not relax their vigilance against the transmission of this highly contagious disease.

The number of COVID-19 infected individuals is increasing rapidly in Cameroon because of the negligence in the implementation of public health measures and non-pharmaceutical strategies, as well as lack of clinical trials to evaluate the best treatment. It is premature to anticipate an end to the outbreak especially in the capital city of Cameroon, Yaoundé, which is currently considered as the epicentre of the disease in the country. The present analysis provided some insights into the potentially dangerous nature of the disease and its consequences, to strengthen decision making.

The differential equations of the SIRD model are given as

The model has four parameters: the transmission rate or the growth rate, β which controls the transition between S and I; the recovery rate γ for hospitalized patients, and the death rate μ. We incorporated social distancing through a constant rate ρ which falls in the interval 0-1, that is expected to decrease the force of infection. We expected that ρ will tend to 1, but we acknowledged the fact that perfect social distancing is difficult to achieve as it directly linked to human behaviour.

In most exponential models the value of R0 is estimated by the expression β/γ+μ

SWY developed the analysis plan, performed the analyses, and drafted the article under the closed supervision of HT. The two authors performed the work for UNITED#COVID-19, the task force of the University of Dschang (Cameroon) for the fight against the novel coronavirus.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.