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Dynamics of novel COVID-19 in the presence of Co-morbidity
Abstract and Figures
A novel coronavirus (COVID-19) has emerged as a global serious public health issue from December 2019. People having a weak immune system are more susceptible to coronavirus infection. It is a double challenge for people of any age with certain underlying medical conditions including cardiovascular disease, diabetes, high blood pressure and cancer etc. Co-morbidity increases the probability of COVID-19 complication. In this paper a deterministic compartmental model is formulated to understand the transmission dynamics of COVID-19. Rigorous mathematical analysis of the model shows that it exhibits backward bifurcation phenomenon when the basic reproduction number is less than unity. For the case of no re-infection it is shown that having the reproduction number less than one is necessary and sufficient for the effective control of COVID-19, that is, the disease free equilibrium is globally asymptotically stable when the reproduction threshold is less than unity. Furthermore, in the absence of reinfection, a unique endemic equilibrium of the model exists which is globally asymptotically stable whenever the reproduction number is greater than unity. Numerical simulations of the model, using data relevant to COVID-19 transmission dynamics, show that the use of efficacious face masks publicly could lead to the elimination of COVID-19 up to a satisfactory level. The study also shows that in the presence of co-morbidity, the disease increases significantly.
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... Before the invention of vaccines, the use of face masks, lock-down, and other non-pharmaceutical interventions and community mitigation strategies (such as: washing and sanitizing hands frequently, and isolation of suspected individuals) were thought to be the effective way to mitigate the disease spread [3,4]. These intervention measures did prove their effectiveness theoretically and mathematically against the pandemic [5,6] but were sometimes insufficient to stop the disease outbreak. So vaccination is thought to be the most effective way to confront this issue and hence vaccinologists worked tirelessly to develop vaccines for preventing At the end of 2020, the first vaccine was approved by World Health Organization (WHO) [7] and it was assumed that vaccination can lead to the end of this pandemic. ...
... Mathematical models can also be analyzed numerically to evaluate the consequences of the new SARS-CoV-2 mutants. There are lots of mathematical models to evaluate the transmission dynamics of COVID-19 [17,6,18,19,20,21,22,16,23,24] and so on. But there are only a few mathematical models to describe the behavior of the COVID-19 wild strain in the presence of its variants of concern [25,26,27,28]. ...
... 0.007, 0.009, 0.006, 0.001 Day -1 Estimated from [36] δ a 2 , δ a 3 , δ q and δ h 0.001, 0.003, 0.004, 0.006 Day -1 Estimated from [36] µ 0.00004 Day -1 [6] Condition-i of Theorem 1 says that the model with the original strain only has a unique endemic equilibrium when R 1 > 1. Using the parameter values as given in table 1 with α = 0 it can be shown that R 1 > 1 which implies there exists a unique endemic equilibrium. ...
Since its inception in December 2019, many safe and effective vaccines have been invented and approved for use against COVID-19 along with various non-pharmaceutical interventions. But the emergence of numerous SARS-CoV-2 variants has put the effectiveness of these vaccines, and other intervention measures under threat. So it is important to understand the dynamics of COVID-19 in the presence of its variants of concern (VOC) in controlling the spread of the disease. To address these situations and to find a way out of this problem, a new mathematical model consisting of a system of non-linear differential equations considering the original COVID-19 strain with its two variants of concern (Delta and Omicron) has been proposed and formulated in this paper. We then analyzed the proposed model to study the transmission dynamics of this multi-strain model and to investigate the consequences of the emergence of multiple new SARS-CoV-2 variants which are more transmissible than the previous ones. The control reproduction number, an important threshold parameter, is then calculated using the next-generation matrix method. Further, we presented the discussion about the stability of the model equilibrium. It is shown that the disease-free equilibrium (DFE) of the model is locally asymptotic stable when the control reproduction is less than unity. It is also shown that the model has a unique endemic equilibrium (EEP) which is locally asymptotic stable when the control reproduction number is greater than unity. Using the Center Manifold theory it is shown that the model also exhibits the backward bifurcation phenomenon when the control reproduction number is less than unity. Again without considering the re-infection of the recovered individuals, it is proved that the disease-free equilibrium is globally asymptotically stable when the reproduction threshold is less than unity. Finally, numerical simulations are performed to verify the analytic results and to show the impact of multiple new SARS-CoV-2 variants in the population which are more contagious than the previous variants. Global uncertainty and sensitivity analysis has been done to identify which parameters have a greater impact on disease dynamics and control disease transmission. Numerical simulation suggests that the emergence of new variants of concern increases COVID-19 infection and related deaths. It also reveals that a combination of non-pharmaceutical interventions with vaccination programs of new more effective vaccines should be continued to control the disease outbreak. This study also suggests that more doses of vaccine should provide to combat new and deadly variants like Delta and Omicron.
... Their mathematical analysis did not mention any possible dynamical behavior likely to be induced by reinfection mechanism, such as the phenomenon of backward bifurcation. [18] investigated dynamics of novel COVID-19 in the presence of co-morbidity with a possibility of reinfection of recovered individuals and found that reinfection could trigger a bi-stability phenomena. However, their paper did not consider a scenario where reinfection may boost an individual natural acquired immunity. ...
... (i) What is the epidemiological implication of boosted infection-acquired immunity? In light of the revelation that reinfection among recovered individuals who have recuperated from COVID-19 can induce the phenomenon of backward bifurcation [18], we shall investigate whether incorporation of a boosted infection-acquired immunity mechanism can induce new bifurcation structures. (ii) Is there any epidemiological insights if there is heterogeneity in infection-acquired immunity among individuals who have recovered from COVID-19? ...
A coronavirus disease 2019 (COVID‐19) epidemiological model incorporating a boosted infection‐acquired immunity and heterogeneity in infection‐acquired immunity among recovered individuals is designed. The model is used to investigate whether incorporating these two processes can induce new epidemiological insights. Analytical findings reveal coexistence of multiple endemic equilibria on either regions divided by the fundamental threshold (control reproduction number). Numerical findings conducted to validate analytical results show that heterogeneity in infection‐acquired immunity among recovered individuals can induce various bifurcation structures such as reversed backward bifurcation , forward bifurcation , backward bifurcation , and reversed hysteresis effect. Moreover, numerical results show that reversed backward bifurcation is annihilated or switches to the usual forward bifurcation if infection‐acquired immunity among recovered individuals with strong immunity is assumed to be everlasting. However, this is only possible if primary infection is more likely than reinfection. In case reinfection is more likely to occur than primary infection, reversed backward bifurcation structure switches to a backward bifurcation phenomenon. Further, longer duration of infection‐acquired immunity does lead to COVID‐19 decline over time but does not lead to flattening of the COVID‐19 peak.
... Their mathematical analysis did not mention any possible dynamical behavior likey to be induced by reinfection mechanism, such as the phenomenon of backward bifurcation. Saha et al. [18] investigated dynamics of novel COVID-19 in the presence of co-morbidity with a possibility of reinfection of recovered individuals and found that reinfection could trigger a bistability phenomena. However, their paper did not consider a scenario where reinfection may boost an individual natural acquired immunity. ...
... (i) What is the epidemiolgical implication of boosted infection-acquired immunity? In light of the revelation that reinfection among recovered indviduals who have recuperated from COVID-19 can induce the phenomenon of backward bifurcation [18], we shall investigate whether incorporation of a boosted infection-acquired immunity mechanism can induce new bifurcation structures? ...
A Coronavirus Disease 2019 (COVID-19) epidemiological model incorporating a boosted infection-acquired immunity and heterogeneity in infection-acquired immunity among recovered individuals is designed. The model is used to investigate whether incorporating these two processes can induce new epidemiological insights. Analytical findings reveal co-existence of multiple endemic equilibria on either regions divided by the fundamental threshold (control reproduction number). Numerical findings conducted to validate analytical results show that heterogeneity in infection-acquired immunity among recovered individuals can induce various bifurcation structures such as reversed backward bifurcation , forward bifurcation , backward bifurcation and reversed hysteresis effect. Moreover, numerical results show that reversed backward bifurcation is annihilated or switches to the usual forward bifurcation if infection-acquired immunity among recovered individuals with strong immunity is assumed to be everlasting. However, this is only possible if primary infection is more likely than reinfection. In case reinfection is more likely to occur than primary infection, reversed backward bifurcation structure switches to a backward bifurcation phenomenon. Further, longer duration of infection-acquired immunity does lead to COVID-19 decline over time but does not lead to flattening of the COVID-19 peak.
... A survey from the US revealed that 5-6 out of 10 adults intended to continue wearing a face mask or using other preventive measures after receiving the first dose [38]. Studies on the cessation of the use of masks in patients with diabetes after being vaccinated against COVID-19 are not available, despite the importance of discontinuing the use of face masks in any population, and even more, in patients with diabetes because of their greater predisposition to complications and risk of dying from COVID-19 [39]. Although today the use of masks is no longer mandatory in Mexico and other regions, the study of the cessation of mask use still provides essential and valuable information. ...
Studies on the cessation of face mask use after a COVID-19 vaccine in patients with diabetes are not available, despite their greater predisposition to complications. We estimated the prevalence of cessation of face mask use after receiving the COVID-19 vaccine in patients with diabetes and identified which factor was most strongly associated with non-use. This was a cross-sectional study in patients with diabetes 18–70 years with at least one dose of vaccine against COVID-19 (n = 288). Participants were asked to respond face-to-face to a questionnaire in a primary care center. Descriptive statistics, chi-square tests, and multivariate binary logistic regression were used for analyzing the association between vulnerability, benefits, barriers, self-efficacy, vaccine expectations (independent variables), and cessation of use (dependent variable), controlling for sociodemographic, smoking, medical, vaccine, and COVID-19 history. The prevalence of cessation of face masks was 25.3% (95% CI 20.2, 30.5). Not feeling vulnerable to hospitalization increased the odds of non-use (adjusted OR = 3.3, 95% CI 1.2, 8.6), while perceiving benefits did the opposite (adjusted OR = 0.4, 95% CI 0.2, 0.9). The prevalence was low, and only two factors were associated with the cessation of face mask use after COVID-19 vaccination in patients with type 2 diabetes.
SARS COV-2 (COVID-19) has a imposed remarkable socio-economic burden and its
impact is still being felt today. In the thesis paper, firstly, we have considered a de-
terministic model that emphasizes the impact of vaccination on the ongoing epidemic
and describe the dynamics of COVID-19 transmission. The suggested model takes
into account the recent findings on COVID-19, such as reinfection, waning of vacci-
nation immunity and infectiousness of those who are asymptomatic, to describe the
dynamics of the disease.
The novel coronavirus disease (COVID-19) caused by SARS-CoV-2 remains a major public health concern globally. In this article, we developed and analyzed an epidemic model of COVID-19 with the impact of vaccination governed by a five system of ordinary differential equations. The developed model is analyzed and the threshold quantity known as the effective reproduction number V R is obtained by using the next generation matrix. We investigate the equilibrium stability of the system, and the disease-free equilibrium is said to be locally asymptotically stable when the effective reproduction number is less than unity, and unstable otherwise. It is observed that the system undergoes the phenomenon of backward bifurcation. Numerical simulations of the overall system are implemented in MATLAB for demonstration of the theoretical results.
In this paper, a deterministic compartmental model is presented to assess the impact of vaccination and non-pharmaceutical interventions (social distance, awareness, face mask, and quarantine) on the transmission dynamics of COVID-19 with co-morbidity and re-infection. An expression for the basic reproduction number is then derived for this model. Theoretical analysis shows that the model exhibits backward bifurcation phenomenon when the basic reproduction number is less than unity. But for the case of no re-infection, the model has a globally asymptotically stable disease-free equilibrium (DFE) when the basic reproduction number is less than unity. Furthermore, it is shown that in the case of no re-infection, a unique endemic equilibrium point (EEP) of the model exists which is globally asymptotically stable whenever the reproduction number is greater than unity. From the global sensitivity and uncertainty analysis, we have identified mask coverage, mask efficacy, vaccine coverage, vaccine efficacy, and contact rate as the most influential parameters influencing the spread of COVID-19. Numerical simulation results show that the use of effective vaccines with proper implementation of non-pharmaceutical interventions could lead to the elimination of COVID-19 from the community. Numerical simulations also suggest that the control strategy that ensures a continuous and effective mass vaccination program is the most cost-effective control strategy. The study also shows that in the presence of any co-morbidity and with the occurrence of re-infection, the disease burden may increase.
Multiple effective vaccines are currently being deployed to combat the COVID-19 pandemic, and are viewed as the major factor in marked reductions of disease burden in regions with moderate to high vaccination coverage. The effectiveness of COVID-19 vaccination programs is, however, significantly threatened by the emergence of new SARS-COV-2 variants that, in addition to being more transmissible than the wild-type (original) strain, may at least partially evade existing vaccines. A two-strain (one wild-type, one variant) and two-group (vaccinated or otherwise) mechanistic mathematical model is designed and used to assess the impact of the vaccine-induced cross-protective efficacy on the spread the COVID-19 pandemic in the United States. Rigorous analysis of the model shows that, in the absence of any co-circulating SARS-CoV-2 variant, the vaccine-derived herd immunity threshold needed to eliminate the wild-type strain can be achieved if 59% of the US population is fully-vaccinated with either the Pfizer or Moderna vaccine. This threshold increases to 76% if the wild-type strain is co-circulating with the Alpha variant (a SARS-CoV-2 variant that is 56% more transmissible than the wild-type strain). If the wild-type strain is co-circulating with the Delta variant (which is estimated to be 100% more transmissible than the wild-type strain), up to 82% of the US population needs to be vaccinated with either of the aforementioned vaccines to achieve the vaccine-derived herd immunity. Global sensitivity analysis of the model reveal the following four parameters as the most influential in driving the value of the reproduction number of the variant strain (hence, COVID-19 dynamics) in the US: (a) the infectiousness of the co-circulating SARS-CoV-2 variant, (b) the proportion of individuals fully vaccinated (using Pfizer or Moderna vaccine) against the wild-type strain, (c) the cross-protective efficacy the vaccines offer against the variant strain and (d) the modification parameter accounting for the reduced infectiousness of fully-vaccinated individuals experiencing breakthrough infection. Specifically, numerical simulations of the model show that future waves or surges of the COVID-19 pandemic can be prevented in the US if the two vaccines offer moderate level of cross-protection against the variant (at least 67%). This study further suggests that a new SARS-CoV-2 variant can cause a significant disease surge in the US if (i) the vaccine coverage against the wild-type strain is low (roughly <66%) (ii) the variant is much more transmissible (e.g., 100% more transmissible), than the wild-type strain, or (iii) the level of cross-protection offered by the vaccine is relatively low (e.g., less than 50%). A new SARS-CoV-2 variant will not cause such surge in the US if it is only moderately more transmissible (e.g., the Alpha variant, which is 56% more transmissible) than the wild-type strain, at least 66% of the population of the US is fully vaccinated, and the three vaccines being deployed in the US (Pfizer, Moderna, and Johnson & Johnson) offer a moderate level of cross-protection against the variant.
In this work, we develop and analyze a mathematical model for the dynamics of COVID-19 with re-infection in order to assess the impact of prior comorbidity (specifically, diabetes mellitus) on COVID-19 complications. The model is simulated using data relevant to the dynamics of the diseases in Lagos, Nigeria, making predictions for the attainment of peak periods in the presence or absence of comorbidity. The model is shown to undergo the phenomenon of backward bifurcation caused by the parameter accounting for increased susceptibility to COVID-19 infection by comorbid susceptibles as well as the rate of reinfection by those who have recovered from a previous COVID-19 infection. Simulations of the cumulative number of active cases (including those with comorbidity), at different reinfection rates, show infection peaks reducing with decreasing reinfection of those who have recovered from a previous COVID-19 infection. In addition, optimal control and cost-effectiveness analysis of the model reveal that the strategy that prevents COVID-19 infection by comorbid susceptibles is the most cost-effective of all the control strategies for the prevention of COVID-19.
Despite progress in clinical care for patients with coronavirus disease 2019 (COVID-19)1, population-wide interventions are still crucial to manage the pandemic, which has been aggravated by the emergence of new, highly transmissible variants. In this study, we combined the SIDARTHE model2, which predicts the spread of SARS-CoV-2 infections, with a new data-based model that projects new cases onto casualties and healthcare system costs. Based on the Italian case study, we outline several scenarios: mass vaccination campaigns with different paces, different transmission rates due to new variants and different enforced countermeasures, including the alternation of opening and closure phases. Our results demonstrate that non-pharmaceutical interventions (NPIs) have a higher effect on the epidemic evolution than vaccination alone, advocating for the need to keep NPIs in place during the first phase of the vaccination campaign. Our model predicts that, from April 2021 to January 2022, in a scenario with no vaccine rollout and weak NPIs (R0 = 1.27), as many as 298,000 deaths associated with COVID-19 could occur. However, fast vaccination rollouts could reduce mortality to as few as 51,000 deaths. Implementation of restrictive NPIs (R0 = 0.9) could reduce COVID-19 deaths to 30,000 without vaccinating the population and to 18,000 with a fast rollout of vaccines. We also show that, if intermittent open–close strategies are adopted, implementing a closing phase first could reduce deaths (from 47,000 to 27,000 with slow vaccine rollout) and healthcare system costs, without substantive aggravation of socioeconomic losses. Integration of variables to account for different speeds of vaccination rollouts and transmission dynamics of new SARS-CoV-2 strains into the SIDARTHE-V model suggests that maintaining non-pharmaceutical interventions during the COVID-19 vaccination campaign in Italy is essential for minimizing mortality in Italy into 2022.
Background
The dynamics of vaccination against SARS-CoV-2 are complicated by age-dependent factors, changing levels of infection, and the relaxation of non-pharmaceutical interventions (NPIs) as the perceived risk declines, necessitating the use of mathematical models. Our aims were to use epidemiological data from the UK together with estimates of vaccine efficacy to predict the possible long-term dynamics of SARS-CoV-2 under the planned vaccine rollout.
Methods
In this study, we used a mathematical model structured by age and UK region, fitted to a range of epidemiological data in the UK, which incorporated the planned rollout of a two-dose vaccination programme (doses 12 weeks apart, protection onset 14 days after vaccination). We assumed default vaccine uptake of 95% in those aged 80 years and older, 85% in those aged 50–79 years, and 75% in those aged 18–49 years, and then varied uptake optimistically and pessimistically. Vaccine efficacy against symptomatic disease was assumed to be 88% on the basis of Pfizer-BioNTech and Oxford-AstraZeneca vaccines being administered in the UK, and protection against infection was varied from 0% to 85%. We considered the combined interaction of the UK vaccination programme with multiple potential future relaxations (or removals) of NPIs, to predict the reproduction number (R) and pattern of daily deaths and hospital admissions due to COVID-19 from January, 2021, to January, 2024.
Findings
We estimate that vaccination alone is insufficient to contain the outbreak. In the absence of NPIs, even with our most optimistic assumption that the vaccine will prevent 85% of infections, we estimate R to be 1·58 (95% credible intervals [CI] 1·36–1·84) once all eligible adults have been offered both doses of the vaccine. Under the default uptake scenario, removal of all NPIs once the vaccination programme is complete is predicted to lead to 21 400 deaths (95% CI 1400–55 100) due to COVID-19 for a vaccine that prevents 85% of infections, although this number increases to 96 700 deaths (51 800–173 200) if the vaccine only prevents 60% of infections. Although vaccination substantially reduces total deaths, it only provides partial protection for the individual; we estimate that, for the default uptake scenario and 60% protection against infection, 48·3% (95% CI 48·1–48·5) and 16·0% (15·7–16·3) of deaths will be in individuals who have received one or two doses of the vaccine, respectively.
Interpretation
For all vaccination scenarios we investigated, our predictions highlight the risks associated with early or rapid relaxation of NPIs. Although novel vaccines against SARS-CoV-2 offer a potential exit strategy for the pandemic, success is highly contingent on the precise vaccine properties and population uptake, both of which need to be carefully monitored.
Funding
National Institute for Health Research, Medical Research Council, and UK Research and Innovation.
The present paper describes the mathematical modeling and dynamics of a novel corona virus (2019-nCoV). We describe the brief details of interaction among the bats and unknown hosts, then among the peoples and the infections reservoir (seafood market). The seafood marked are considered the main source of infection when the bats and the unknown hosts (may be wild animals) leaves the infection there. The purchasing of items from the seafood market by peoples have the ability to infect either asymptomatically or symptomatically. We reduced the model with the assumptions that the seafood market has enough source of infection that can be effective to infect people. We present the mathematical results of the model and then formulate a fractional model. We consider the available infection cases for January 21, 2020, till January 28, 2020 and parameterized the model. We compute the basic reproduction number for the data is R0≈2.4829. The fractional model is then solved numerically by presenting many graphical results, which can be helpful for the infection minimization.
A mathematical model is designed and used to study the transmission dynamics and control of COVID-19 in Nigeria. The model, which was rigorously analysed and parametrized using COVID-19 data published by the Nigeria Centre for Disease Control (NCDC), was used to assess the community-wide impact of various control and mitigation strategies in some jurisdictions within Nigeria (notably the states of Kano and Lagos, and the Federal Capital Territory, Abuja). Numerical simulations of the model showed that COVID-19 can be effectively controlled in Nigeria using moderate levels of social-distancing strategy in the jurisdictions and in the entire nation. Although the use of face masks in public can significantly reduce COVID-19 in Nigeria, its use, as a sole intervention strategy, may fail to lead to a substantial reduction in disease burden. Such substantial reduction is feasible in the jurisdictions (and the entire Nigerian nation) if the public face mask use strategy is complemented with a social-distancing strategy. The community lockdown measures implemented in Nigeria on March 30, 2020 need to be maintained for at least three to four months to lead to the effective containment of COVID-19 outbreaks in the country. Relaxing, or fully lifting, the lockdown measures sooner, in an effort to re-open the economy or the country, may trigger a deadly second wave of the pandemic. © 2020 American Institute of Mathematical Sciences. All rights reserved.
Background: Coronavirus disease 2019 (COVID-19), the most hectic pandemic of the era, is increasing exponentially and taking thousands of lives worldwide. This study aimed to assess the prevalence of pre-existing comorbidities among COVID-19 patients and their mortality risks with each category of pre-existing comorbidity.
Methods: To conduct this systematic review and meta-analysis, Medline, Web of Science, Scopus, and CINAHL databases were searched using pre-specified search strategies. Further searches were conducted using the reference list of the selected studies, renowned preprint servers (eg, medRxiv, bioRxiv, SSRN), and relevant journals’ websites. Studies written in the English language included if those were conducted among COVID-19 patients with and without comorbidities and presented survivor vs non-survivor counts or hazard/odds of deaths or survivors with types of pre-existing comorbidities. Comorbidities reported in the selected studies were grouped into eight categories. The pooled likelihoods of deaths in each category were estimated using a fixed or random-effect model, based on the heterogeneity assessment. Publication bias was assessed by visual inspection of the funnel plot asymmetry and Egger’s regression test. Trim and Fill method was used if there any publication bias was found.
Results: A total of 41 studies included in this study comprised of 27 670 samples. The most common pre-existing comorbidities in COVID-19 patients were hypertension (39.5%), cardiovascular disease (12.4%), and diabetes (25.2%). The higher likelihood of deaths was found among COVID-19 patients who had pre-existing cardiovascular diseases (odds ratio (OR) = 3.42, 95% confidence interval (CI) = 2.86-4.09), immune and metabolic disorders (OR = 2.46, 95% CI = 2.03-2.85), respiratory diseases (OR = 1.94, 95% CI = 1.72-2.19), cerebrovascular diseases (OR = 4.12, 95% CI = 3.04-5.58), any types of cancers (OR = 2.22, 95% CI = 1.63-3.03), renal (OR = 3.02, 95% CI = 2.60-3.51), and liver diseases (OR = 2.35, 95% CI = 1.50-3.69).
Conclusions: This study provides evidence that COVID-19 patients with pre-existing comorbidities had a higher likelihood of death. These findings could potentially help health care providers to sort out the most susceptible COVID-19 patients by comorbidities, take precautionary measures during hospitalization, assess susceptibility to death, and prioritize their treatment, which could potentially reduce the number of fatalities in COVID-19.
Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision-making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the health care system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.
This work examines the impact of various non-pharmaceutical control measures (government and personal) on the population dynamics of the novel coronavirus disease 2019 (COVID-19) in Lagos, Nigeria, using an appropriately formulated mathematical model. Using the available data, since its first reported case on 16 March 2020, we seek to develop a predicative tool for the cumulative number of reported cases and the number of active cases in Lagos; we also estimate the basic reproduction number of the disease outbreak in the aforementioned State in Nigeria. Using numerical simulations, we show the effect of control measures, specifically the common social distancing, use of face mask and case detection (via contact tracing and subsequent testings) on the dynamics of COVID-19. We also provide forecasts for the cumulative number of reported cases and active cases for different levels of the control measures being implemented. Numerical simulations of the model show that if at least 55% of the population comply with the social distancing regulation with about 55% of the population effectively making use of face masks while in public, the disease will eventually die out in the population and that, if we can step up the case detection rate for symptomatic individuals to about 0.8 per day, with about 55% of the population complying with the social distancing regulations, it will lead to a great decrease in the incidence (and prevalence) of COVID-19.
Countries around the world are implementing lock-down measures in a bid to flatten the curve of the new deadly COVID-19 disease. Our paper does not claim to have found the cure for COVID-19, neither does it claim that the suggested model have taken into account all the complexities around the spread of the disease. Nonetheless, the fundamental question asked in this paper is to know if within the conditions taken into account in this suggested model, the integral lock-down is effective in saving human lives. To answer this question, a mathematical model was suggested taking into account the possibility of transmission of COVID-19 from dead bodies to humans and the effect of lock-down. Three cases were considered. The first case suggested that there is transmission from dead to the living (medical staffs as they perform postmortem procedures on corpses, and direct contacts with during burial ceremonies). This case has no equilibrium points except for disease free equilibrium, a clear indication that care must be taken when dealing with corpses due to corona-19. In the second case we removed the transmission rate from dead bodies. This case showed an equilibrium point, although the number of deaths, carriers and infected grew exponentially up to a certain stability level. In the last case, we incorporated a lock-down and social distancing effect, using the next generation matrix. We could achieve a zero reproduction number, with number of deaths, infected and carriers decaying very rapidly. This is a clear indication that if lock-down recommendations are observed the threat of COVID-19 can be reduced to zero in few months.While our mathematical model agrees with the effectiveness of the lock-down, it is important to mention damaging effects of inadequate testing. The long waiting period of few days before confirmation of status, can only lead to more infections. The asymptomatic tested person could be positive and spread the infection, or could contact the virus in days after testing and will spread the disease further, after being given a false result. Testing kit that with immediate results are needed for more efficient measures. We used Italy’s Data to guide the construction of the mathematical model. To include non-locality into mathematical formulas, differential and integral operators were suggested. Properties and numerical approximations were presented in details. Finally, the suggested differential and integral operators were applied to the model.