Mathematical modelling of COVID-19 transmission and control strategies in the population of Bauchi State, Nigeria

The novel SARS-COV-2 has since been declared a pandemic by the World Health Organization (WHO). The virus has spread from Wuhan city in China in December 2019 to no fewer than 200 countries as at June 2020 and still counting. Nigeria is currently experiencing a rapid spread of the virus amidst weak health system and more than 80% of population leaving on less than 1USD per day. To help understand the behavior of the virus in resource limited settings, we modelled the outbreak of COVID-19 and effects of control strategies in Bauchi state at north-eastern Nigeria. Using the real data of Bauchi state COVID-19 project, this research work extends the epidemic SEIR model by introducing new parameters based on the transmission dynamics of the novel COVID-19 pandemic and preventive measures. The total population of Bauchi State at the time of the study, given by is compartmentalized into five (5) different compartments as follows: Susceptible (S), Exposed (E), Infectious (I), Quarantined (Q) and Recovered (R). The new model is SEIQR. N = S → E → I → Q → R Data was collected by accessing Bauchi state electronic database of COVID-19 project to derive all the model parameters, while analysis and model building was done using Maple software. At the time of this study, it was found that the reproduction number R, for COVID-19 in Bauchi state, is 2.6 × 10-5. The reproduction number R decreased due to the application of control measures. The compartmental SEIRQ model in this study, which is a deterministic system of linear differential equations, has a continuum of disease-free equilibria, which is rigorously shown to be locallyasymptotically stable as the epidemiological threshold, known as the control reproduction number R= 0.0000026 is less than unity. The implication of this study is that the COVID-19 pandemic can be effectively controlled in Bauchi, since is R<1. Contact tracing and isolation must be increased as the models shows, the rise in infected class is a sign of high vulnerability of the population. Unless control measures are stepped up, despite high rate of recovery as shown by this study, infection rate will keep increasing as currently there is a no vaccine for COVID-19.

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SEAMHCRD deterministic compartmental model based on clinical stages of infection for COVID-19 pandemic in Sultanate of Oman

10.21203/rs.3.rs-91097/v1 ◽

2020 ◽

Author(s):

Abraham Varghese ◽

Shajidmon Kolamban ◽

Vinu Sherimon ◽

Eduardo M. Lacap ◽

Saad Salman Ahmed ◽

...

Keyword(s):

Basic Reproduction Number ◽

Compartmental Model ◽

Reproduction Number ◽

Research Work ◽

Contact Tracing ◽

Model Parameters ◽

Policy Makers ◽

Estimated Parameters ◽

Short Period ◽

Reported Data

Abstract The present novel corona virus (COVID-19) infection has engendered a worldwide crisis across the world in an enormous scale within a very short period. The effective solution for this pandemic is to recognize the nature and spread of the disease so that appropriate policies can be framed. Mathematical modelling is always at the forefront to understand and provide an adequate description about the transmission of any disease. In this research work, we have formulated a deterministic compartmental model (SEAMHCRD) including various stages of infection, such as Mild, Moderate, Severe and Critical to study the spreading of COVID-19 and estimated the model parameters by fitting the model with the reported data of ongoing pandemic in Oman. The steady state, stability and final pandemic size of the model has been proved mathematically. The various transmission as well as transition parameters are estimated during the period from June 8th - July 30th, 2020. Based on the current estimated parameters, the pandemic size is also predicted for another 100 days. Sensitivity analysis is performed to identify the key model parameters, and corresponding basic reproduction number has been computed using Next Generation Matrix (NGM) method. As the value of basic reproduction number (R0) is 0.9761 during the period from June 8th - July 30th, 2020, it is an indication for the policy makers to adopt appropriate remedial measures like social distancing and contact tracing to reduce the value of R0 to control the spread of the disease.

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TRANSMISSION DYNAMICS AND CONTROL STRATEGIES OF COVID-19 IN WUHAN, CHINA

Journal of Biological System ◽

10.1142/s0218339020500096 ◽

2020 ◽

Vol 28 (03) ◽

pp. 543-560 ◽

Cited By ~ 8

Author(s):

LIUYONG PANG ◽

SANHONG LIU ◽

XINAN ZHANG ◽

TIANHAI TIAN ◽

ZHONG ZHAO

Keyword(s):

Reproduction Number ◽

Control Strategies ◽

Public Awareness ◽

Control Measures ◽

Transmission Dynamics ◽

Published Data ◽

Model Parameters ◽

Strict Control ◽

Dynamics And Control ◽

Numerical Calculation Method

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the transmission dynamics and was applied to fit the published data on the confirmed cases of Wuhan city from December 31, 2019 to March 25, 2020 to deduce the time when the first patient with COVID-19 appeared. The basic reproduction number was estimated in the first stage to demonstrate the number of secondary infectious cases generated by an average infectious case in the absence of policy intervention. The effective reproduction numbers in second and third stages were estimated to evaluate the effects of the two strict control measures. In addition, sensitivity analysis of the reproduction number according to model parameters was executed to demonstrate the effect of the control measures for containing the spread of COVID-19. Finally, the numerical calculation method was applied to investigate the influence of the different control measures on the spread of COVID-19. The results indicated that following the strict quarantine rule was very effective, and reducing the effective contact rates and improving the diagnosis rate were crucial in reducing the effective reproduction number, and taking control measures as soon as possible can effectively contain a larger outbreak of COVID-19. But a bigger challenge for us to contain the spread of COVID-19 was the transmission from the asymptomatic carriers, which required to raising the public awareness of self-protection and keeping a good physical protection.

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Analysis of Potential Risk of COVID-19 Infections in China Based on a Pairwise Epidemic Model

10.20944/preprints202002.0398.v1 ◽

2020 ◽

Cited By ~ 1

Author(s):

Xiaofeng Luo ◽

Shanshan Feng ◽

Junyuan Yang ◽

Xiao-Long Peng ◽

Xiaochun Cao ◽

...

Keyword(s):

Epidemic Model ◽

Reproduction Number ◽

Economic Benefits ◽

Control Measures ◽

Contact Tracing ◽

The Novel ◽

The Public ◽

Disease Propagation ◽

Long Run ◽

Novel Coronavirus

The ongoing outbreak of the novel coronavirus pneumonia (also known as COVID-19) has triggered a series of stringent control measures in China, such as city closure, traffic restrictions, contact tracing and household quarantine. These containment efforts often lead to changes in the contact pattern among individuals of the population. Many existing compartmental epidemic models fail to account for the effects of contact structure. In this paper, we devised a pairwise epidemic model to analyze the COVID-19 outbreak in China based on confirmed cases reported during the period February 3rd--17th, 2020. By explicitly incorporating the effects of family clusters and contact tracing followed by household quarantine and isolation, our model provides a good fit to the trajectory of COVID-19 infections and is useful to predict the epidemic trend. We obtained the average of the reproduction number $R=1.494$ ($95\%$ CI: $1.483-1.507$) for Hubei province and $R=1.178$ ($95\%$ CI: $1.145-1.158$) for China (except Hubei), suggesting that some existing studies may have overestimated the reproduction number by neglecting the dynamical correlations and clustering effects. We forecasted that the COVID-19 epidemic would peak on February 13th ($95\%$ CI: February $9-17$th) in Hubei and 6 days eariler in the regions outside Hubei. Moreover the epidemic was expected to last until the middle of March in China (except Hubei) and late April in Hubei. The sensitivity analysis shows that ongoing exposure for the susceptible and population clustering play an important role in the disease propagation. With the enforcement of household quarantine measures, the reproduction number $R$ effectively reduces and epidemic quantities decrease accordingly. Furthermore, we gave an answer to the public concern on how long the stringent containment strategies should maintain. Through numerical analysis, we suggested that the time for the resumption of work and production in China (except Hubei) and Hubei would be the middle of March and the end of April, 2020, respectively. These constructive suggestions may bring some immeasurable social-economic benefits in the long run.

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Investigating the effectiveness of re-opening policies before vaccination during a pandemic: SD modelling research based on COVID-19 in Wuhan

BMC Public Health ◽

10.1186/s12889-021-11631-w ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Ying Qian ◽

Wei Xie ◽

Jidi Zhao ◽

Ming Xue ◽

Shiyong Liu ◽

...

Keyword(s):

Model Simulation ◽

Control Measures ◽

World Health ◽

Contact Tracing ◽

Infection Prevention And Control ◽

Real World Data ◽

Medical Resources ◽

Health Organization ◽

The Impact ◽

Different Levels

Abstract Background Lockdown policies were widely adopted during the coronavirus disease 2019 (COVID-19) pandemic to control the spread of the virus before vaccines became available. These policies had significant economic impacts and caused social disruptions. Early re-opening is preferable, but it introduces the risk of a resurgence of the epidemic. Although the World Health Organization has outlined criteria for re-opening, decisions on re-opening are mainly based on epidemiologic criteria. To date, the effectiveness of re-opening policies remains unclear. Methods A system dynamics COVID-19 model, SEIHR(Q), was constructed by integrating infection prevention and control measures implemented in Wuhan into the classic SEIR epidemiological model and was validated with real-world data. The input data were obtained from official websites and the published literature. Results The simulation results showed that track-and-trace measures had significant effects on the level of risk associated with re-opening. In the case of Wuhan, where comprehensive contact tracing was implemented, there would have been almost no risk associated with re-opening. With partial contact tracing, re-opening would have led to a minor second wave of the epidemic. However, if only limited contact tracing had been implemented, a more severe second outbreak of the epidemic would have occurred, overwhelming the available medical resources. If the ability to implement a track-trace-quarantine policy is fixed, the epidemiological criteria need to be further taken into account. The model simulation revealed different levels of risk associated with re-opening under different levels of track-and-trace ability and various epidemiological criteria. A matrix was developed to evaluate the effectiveness of the re-opening policies. Conclusions The SEIHR(Q) model designed in this study can quantify the impact of various re-opening policies on the spread of COVID-19. Integrating epidemiologic criteria, the contact tracing policy, and medical resources, the model simulation predicts whether the re-opening policy is likely to lead to a further outbreak of the epidemic and provides evidence-based support for decisions regarding safe re-opening during an ongoing epidemic. Keyords COVID-19; Risk of re-opening; Effectiveness of re-opening policies; IPC measures; SD modelling.

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Face masks are an essential tool to mitigate the ongoing SARS-CoV-2 pandemic: a call to action

Rhinology online ◽

10.4193/rhinol/20.065 ◽

2020 ◽

Vol 3 (3) ◽

pp. 157-159

Author(s):

P. Dehgani-Mobaraki ◽

A. Kamber Zaidi ◽

J.M. Levy ◽

Keyword(s):

Upper Airway ◽

World Health ◽

Contact Tracing ◽

The Novel ◽

Call To Action ◽

Public Health Emergencies ◽

Current Spread ◽

The World ◽

Health And Disease ◽

Novel Coronavirus

Over the past several months, an increasing volume of infor- mation has expanded awareness regarding the transmission of SARS-CoV-2, the novel coronavirus associated with COVID-19. Following the pandemic declaration by the World Health Orga- nization (WHO), global authorities immediately took measures to reduce the transmission and subsequent morbidity associa- ted with this highly contagious disease. However, despite initial success in “flattening the curve” of viral transmission, many areas of the world are currently experiencing an increase in com- munity transmission, threatening to replicate the early public health emergencies experienced by Italy (1,2). In addition, the possibility of contact tracing through geosocial applications and public service platforms have been met with variable interest (3). Given current spread and the upcoming influenza season, it is essential that we use our voices as experts in upper airway health and disease to educate and encourage all communities to adopt appropriate protective measures, including the routine use of facemasks.

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Modelling and Simulating the Novel Coronavirus with Implications of Asymptomatic Carriers

International Journal of Differential Equations ◽

10.1155/2020/5487147 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Ghassane Benrhmach ◽

Khalil Namir ◽

Jamal Bouyaghroumni

Keyword(s):

Control Strategies ◽

World Health ◽

Contact Tracing ◽

Effective Control ◽

Public Authorities ◽

Asymptomatic Carriers ◽

Social Distancing ◽

Infected People ◽

Novel Coronavirus ◽

Health Organization

The World Health Organization declared that the total number of confirmed cases tested positive for SARS‐CoV‐2, affecting 210 countries, exceeded 3 million on 29 April 2020, with more than 207,973 deaths. In order to end the global COVID‐19 pandemic, public authorities have put in place multiple strategies like testing, contact tracing, and social distancing. Predictive mathematical models for epidemics are fundamental to understand the development of the epidemic and to plan effective control strategies. Some hosts may carry SARS‐CoV‐2 and transmit it to others, yet display no symptoms themselves. We propose applying a model (SELIAHRD) taking in consideration the number of asymptomatic infected people. The SELIAHRD model consists of eight stages: Susceptible, Exposed, Latent, Symptomatic Infected, Asymptomatic Infected, Hospitalized, Recovered, and Dead. The asymptomatic carriers contribute to the spread of disease, but go largely undetected and can therefore undermine efforts to control transmission. The simulation of possible scenarios of the implementation of social distancing shows that if we rigorously follow the social distancing rule then the healthcare system will not be overloaded.

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Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/8869377 ◽

2020 ◽

Vol 2020 ◽

pp. 1-21

Author(s):

Aristide G. Lambura ◽

Gasper G. Mwanga ◽

Livingstone Luboobi ◽

Dmitry Kuznetsov

Keyword(s):

Optimal Control ◽

Equilibrium Point ◽

Drug Administration ◽

Mass Drug Administration ◽

Helminth Infection ◽

Reproduction Number ◽

Control Strategies ◽

Active Tuberculosis ◽

Control Measures ◽

The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

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Genealogy of Resistant Tuberculosis in Latin America and the Caribbean until 2020

10.5772/intechopen.96280 ◽

2021 ◽

Author(s):

Onix J. Cantres-Fonseca ◽

Francisco Del Olmo-Arroyo

Keyword(s):

Latin America ◽

Multidrug Resistance ◽

Drug Exposure ◽

Control Strategies ◽

Treatment Resistance ◽

High Rate ◽

World Health ◽

Resistant Tuberculosis ◽

The World ◽

The Caribbean

History hallmarks different out brakes events during the last century. Being caught in the in the middle of the catastrophic COVID-19 pandemic, that initiated in 2019 makes possible to forget other causalities. Tuberculosis makes the case. The pathogen has been present more than hundredth years. Relevance rest in worldwide prevalence, pathogen spread, treatment resistance and the need for eradication. Drug treatment resistance is considered as one of the criteria to prioritize a country in the World Health Organization’s intention to eradicate tuberculosis infection in the world. For decades in Latin America, including the Caribbean, there have been a persistent high rate of drug resistance with an overall prevalence to one or more drug rounds 13.0%. Approximately 30% of previously treated cases have a multidrug resistance. In this chapter, we intend to review the epidemiology of resistant tuberculosis, and the causes of resistance associated to the community of people in the Latin American and the Caribbean. We intend to describe the genetic response of Mycobacterium tuberculosis from its migratory journey throughout decades from areas of Europa and Asia to Latin America, its genetic transformation secondary to inadequate drug exposure and the characteristics of the infected host, and how a change in the healthcare system and tuberculosis control strategies access are needed to change the surge of multidrug resistance tuberculosis.

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Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics

10.1101/2020.04.10.20060954 ◽

2020 ◽

Cited By ~ 3

Author(s):

Gabriel G. Katul ◽

Assaad Mrad ◽

Sara Bonetti ◽

Gabriele Manoli ◽

Anthony J. Parolari

Keyword(s):

Global Convergence ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Control Strategies ◽

Early Period ◽

Early Time ◽

World Health ◽

Potential Control ◽

The Usa ◽

Early Phases

AbstractThe SIR (‘susceptible-infectious-recovered’) formulation is used to uncover the generic spread mechanisms observed by COVID-19 dynamics globally, especially in the early phases of infectious spread. During this early period, potential controls were not effectively put in place or enforced in many countries. Hence, the early phases of COVID-19 spread in countries where controls were weak offer a unique perspective on the ensemble-behavior of COVID-19 basic reproduction number Ro. The work here shows that there is global convergence (i.e. across many nations) to an uncontrolled Ro = 4.5 that describes the early time spread of COVID-19. This value is in agreement with independent estimates from other sources reviewed here and adds to the growing consensus that the early estimate of Ro = 2.2 adopted by the World Health Organization is low. A reconciliation between power-law and exponential growth predictions is also featured within the confines of the SIR formulation. Implications for evaluating potential control strategies from this uncontrolled Ro are briefly discussed in the context of the maximum possible infected fraction of the population (needed for assessing health care capacity) and mortality (especially in the USA given diverging projections). Model results indicate that if intervention measures still result in Ro> 2.7 within 49 days after first infection, intervention is unlikely to be effective in general for COVID-19. Current optimistic projections place mortality figures in the USA in the range of 100,000 fatalities. For fatalities to be confined to 100,000 requires a reduction in Ro from 4.5 to 2.7 within 17 days of first infection assuming a mortality rate of 3.4%.

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COVID-19 Pandemic in India: A Mathematical Model Study

10.20944/preprints202005.0508.v1 ◽

2020 ◽

Author(s):

Sudhanshu Kumar Biswas ◽

Jayanta Kumar Ghosh ◽

Susmita Sarkar ◽

Uttam Ghosh

Keyword(s):

Population Density ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Virus Disease ◽

Control Measures ◽

High Population ◽

Model Parameters ◽

High Population Density ◽

Corona Virus ◽

Very High

The present novel corona virus (2019-nCoV) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. The infection induced death rate is also very high. There is no vaccine or anti-viral medicine for such infection. So at this moment a major worldwide problem is that how we can control this pandemic. On the other hand, India is a high population density country, where the corona virus disease (COVID-19) has started to spread from $1^{st}$ week of March, 2020 in a significant number of COVID-19 positive cases. Due to this high population density human to human social contact rate is very high in India. So control of the pandemic COVID-19 in early stage is very urgent and challenging problem. Mathematical models are employed in this paper to study the COVID-19 dynamics, to identify the influential parameters and to find the proper prevention strategies to reduce the outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the key model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impacts on the disease dynamics have also been studied. Future trends of the disease transmission has been Predicted from our model with some control measures. Finally, the positive measures to control the disease have been summarized.

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