MATHEMATICAL PREDICTIONS FOR COVID-19 AS A GLOBAL PANDEMIC

Reproductive Number ◽

Government Decision ◽

Global Pandemic ◽

Secondary Infections ◽

Rate Of Recovery ◽

Precautionary Measures ◽

The Moment ◽

ABSTRACTThis study shows that the disease free equilibrium (E0) for COVID-19 coronavirus does not satisfy the criteria for a locally or globally asymptotic stability. This implies that as a pandemic as declared by WHO (2020) the COVID-19 coronavirus does not have a curative vaccine yet and precautionary measures are advised through quarantine and observatory procedures. Also, the Basic Reproductive number (R0 < 1) by Equation (33) shows that there is a chance of decline of secondary infections when the ratio between the incidence rate in the population and the total number of infected population quarantined with observatory procedure.The effort to evaluate the disease equilibrium shows that unless there is a dedicated effort from government, decision makers and stakeholders, the world would hardly be reed of the COVID-19 coronavirus and further spread is eminent and the rate of infection will continue to increase despite the increased rate of recovery because of the absence of vaccine at the moment.

Mathematical Predictions for Covid-19 as a Global Pandemic (Preprint)

10.2196/preprints.19166 ◽

2020 ◽

Cited By ~ 2

Author(s):

Alexander Okhuese Victor

Keyword(s):

Recovery Rate ◽

Reproductive Number ◽

Policy Makers ◽

Infected Population ◽

Global Pandemic ◽

Secondary Infections ◽

Rate Of Recovery ◽

Precautionary Measures ◽

Model Equations

UNSTRUCTURED The model equations which exhibits the disease-free equilibrium (E_0 ) state for COVID-19 coronavirus does not exist and hence does not satisfy the criteria for a locally or globally asymptotic stability when the basic reproductive number R_0=1 for and endemic situation. This implies that the COVID-19 coronavirus does not have a curative vaccine yet and precautionary measures are advised through quarantine and observatory procedures. The basic reproductive number was found to be R_0<1 and hence shows that there is a chance of decline of secondary infections when the ratio between the incidence rate in the population and the total number of infected population quarantined with observatory procedure. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect of the implementation of quarantine and observatory procedures has on the projection of the further spread of the virus globally. Result shows that the proportion of infected population in the absence of curative vaccination will continue to grow globally meanwhile the recovery rate will continue slowly which therefore means that the ratio of infection to recovery rate will determine the death rate that is recorded globally. Therefore, the effort to evaluate the disease equilibrium shows that unless there is a dedicated effort from individual population, government, health organizations, policy makers and stakeholders, the world would hardly be reed of the COVID-19 coronavirus and further spread is eminent and the rate of infection will continue to increase despite the increased rate of recovery until a curative vaccine is developed.

Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

Asian Research Journal of Mathematics ◽

10.9734/arjom/2020/v16i730199 ◽

2020 ◽

pp. 8-19

Author(s):

Laid Chahrazed

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Reproductive Number ◽

Globally Asymptotically Stable ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

The Stability ◽

Disease Free ◽

Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

Estimation of the probability of reinfection with COVID-19 coronavirus by the SEIRUS model

10.1101/2020.04.02.20050930 ◽

2020 ◽

Author(s):

Victor Alexander Okhuese

Keyword(s):

Recovery Rate ◽

Death Rate ◽

Reproductive Number ◽

Chain Reaction ◽

Health Community ◽

Polymerase Chain ◽

Model Equations ◽

Disease Free ◽

Pcr Test

AbstractWith sensitivity of the Polymerase Chain Reaction (PCR) test used to detect the presence of the virus in the human host, the global health community has been able to record a great number of recovered population. Therefore, in a bid to answer a burning question of reinfection in the recovered class, the model equations which exhibits the disease-free equilibrium (E0) state for COVID-19 coronavirus was developed in this study and was discovered to both exist as well as satisfy the criteria for a locally or globally asymptotic stability with a basic reproductive number R0 = 0 for and endemic situation. Hence, there is a chance of no secondary reinfections from the recovered population as the rate of incidence of the recovered population vanishes, that is, B = 0.Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect of the implementation of quarantine and observatory procedures has on the projection of the further spread of the virus globally. Result shows that the proportion of infected population in the absence of curative vaccination will continue to grow globally meanwhile the recovery rate will continue slowly which therefore means that the ratio of infection to recovery rate will determine the death rate that is recorded globally and most significant for this study is the rate of reinfection by the recovered population which will decline to zero over time as the virus is cleared clinically from the system of the recovered class.

TRANSMISSION DYNAMICS OF DENGUE IN COSTA RICA: THE ROLE OF HOSPITALIZATIONS

Revista de Matemática Teoría y Aplicaciones ◽

10.15517/rmta.v27i1.39977 ◽

2019 ◽

Vol 27 (1) ◽

pp. 241-266

Author(s):

FABIO SANCHEZ ◽

JORGE ARROYO-ESQUIVEL ◽

PAOLA VÁSQUEZ

Keyword(s):

Costa Rica ◽

Compartmental Model ◽

Control Strategies ◽

Transmission Dynamics ◽

Reproductive Number ◽

Specific Parameter ◽

Public Health Officials ◽

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, R0, is computed, as well as a sensitivity analysis on R0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.

Mathematical modelling for malaria under resistance and population movement

Revista Integración ◽

10.18273/revint.v38n2-2020006 ◽

2020 ◽

Vol 38 (2) ◽

pp. 133-163

Author(s):

Cristhian Montoya ◽

Jhoana P. Romero Leiton

Keyword(s):

Human Population ◽

Control Strategies ◽

Reproductive Number ◽

Transmission Dynamic ◽

Equilibrium Solutions ◽

Population Movements ◽

Existence And Stability ◽

Theoretical Results ◽

In this work, two mathematical models for malaria under resistance are presented. More precisely, the first model shows the interaction between humans and mosquitoes inside a patch under infection of malaria when the human population is resistant to antimalarial drug and mosquitoes population is resistant to insecticides. For the second model, human–mosquitoes population movements in two patches is analyzed under the same malaria transmission dynamic established in a patch. For a single patch, existence and stability conditions for the equilibrium solutions in terms of the local basic reproductive number are developed. These results reveal the existence of a forward bifurcation and the global stability of disease–free equilibrium. In the case of two patches, a theoretical and numerical framework on sensitivity analysis of parameters is presented. After that, the use of antimalarial drugs and insecticides are incorporated as control strategies and an optimal control problem is formulated. Numerical experiments are carried out in both models to show the feasibility of our theoretical results.

Impact of Awareness to Control Malaria Disease: A Mathematical Modeling Approach

Complexity ◽

10.1155/2020/8657410 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Malik Muhammad Ibrahim ◽

Muhammad Ahmad Kamran ◽

Malik Muhammad Naeem Mannan ◽

Sangil Kim ◽

Il Hyo Jung

Keyword(s):

Mathematical Modeling ◽

Numerical Technique ◽

Reproductive Number ◽

Awareness Campaign ◽

Runge Kutta Method ◽

Proposed Model ◽

Awareness Programs ◽

Disease Free ◽

Differential Process

The mathematical modeling of malaria disease has a crucial role in understanding the insights of the transmission dynamics and corresponding appropriate prevention strategies. In this study, a novel nonlinear mathematical model for malaria disease has been proposed. To prevent the disease, we divided the infected population into two groups, unaware and aware infected individuals. The growth rate of awareness programs impacting the population is assumed to be proportional to the unaware infected individuals. It is further assumed that, due to the effect of awareness campaign, the aware infected individuals avoid contact with mosquitoes. The positivity and the boundedness of solutions have been derived through the completing differential process. Local and global stability analysis of disease-free equilibrium has been investigated via basic reproductive number R0, if R0 < 1, the system is stable otherwise unstable. The existence of the unique endemic equilibrium has been also determined under certain conditions. The solution to the proposed model is derived through an iterative numerical technique, the Runge–Kutta method. The proposed model is simulated for different numeric values of the population of humans and anopheles in each class. The results show that a significant increase in the population of susceptible humans is achieved in addition to the decrease in the population of the infected mosquitoes.

Global Stability of an SEIS Epidemic Model with General Saturation Incidence

ISRN Applied Mathematics ◽

10.1155/2013/710643 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Hui Zhang ◽

Li Yingqi ◽

Wenxiong Xu

Keyword(s):

Latent Period ◽

Epidemic Model ◽

Convergence Theorem ◽

Incidence Rates ◽

Reproductive Number ◽

Global Dynamics ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

We present an SEIS epidemic model with infective force in both latent period and infected period, which has different general saturation incidence rates. It is shown that the global dynamics are completely determined by the basic reproductive number R0. If R0≤1, the disease-free equilibrium is globally asymptotically stable in T by LaSalle’s Invariance Principle, and the disease dies out. Moreover, using the method of autonomous convergence theorem, we obtain that the unique epidemic equilibrium is globally asymptotically stable in T0, and the disease spreads to be endemic.

A MODEL FOR VECTOR TRANSMITTED DISEASES WITH SATURATION INCIDENCE

Journal of Biological System ◽

10.1142/s0218339001000414 ◽

2001 ◽

Vol 09 (04) ◽

pp. 235-245 ◽

Cited By ~ 21

Author(s):

LOURDES ESTEVA ◽

MARIANO MATIAS

Keyword(s):

Endemic Equilibrium ◽

Saturation Effect ◽

Infected Host ◽

Reproductive Number ◽

The Stability ◽

Stability Results ◽

A model for a disease that is transmitted by vectors is formulated. All newborns are assumed susceptible, and human and vector populations are assumed to be constant. The model assumes a saturation effect in the incidences due to the response of the vector to change in the susceptible and infected host densities. Stability of the disease free equilibrium and existence, uniqueness and stability of the endemic equilibrium is investigated. The stability results are given in terms of the basic reproductive number R0.

Mathematical Analysis A Continuous Vaccination Strategy Effect against to spread of Measles by Using the Epidemic SVIR Models

10.31219/osf.io/5zyqb ◽

2017 ◽

Author(s):

Tonaas Kabul Wangkok Yohanis Marentek

Keyword(s):

Fixed Point ◽

Vaccination Strategy ◽

Fixed Time ◽

Necessary Condition ◽

Reproductive Number ◽

Time Interval ◽

Asymptotically Stable ◽

Fixed Time Interval ◽

Vaccination is one way to minimize the spread of disease. To complete a vaccination, it is usually done several times and there should be a fixed time interval. Considering vaccination in the basic SIR model, SVIR model assumes that individuals are vaccinated do not get immediate immunity means that individuals who are vaccinated still allow infected. So according to the process of vaccination on SVIR model, there are two strategies which continuous vaccination strategy (CVS) and disconnected vaccination strategy (PVS). In this study only addressed continuous vaccination strategy in epidemic model SVIR. Results from the study indicate that the dynamics of the CVS system is fully dependent on the basic reproductive number. If the basic reproductive number is less than one then the fixed point asymptotically stable disease-free will which means that eventually the disease will disappear from the population. Conversely, if more than one fixed point is asymptotically stable endemic would mean that the disease will still exist in the population. Mathematical results show that vaccination helps to minimize the spread of disease by reducing the basic reproductive number. But there is a necessary condition for the disease can be eradicated. If the time for the vaccine recipients to obtain immunity or the possibility of vaccine recipients infected neglected, the condition of the disease will disappear and the disease will always be eradicated. This can lead to over-evaluating the effect of vaccination.

Transmission dynamics of SARS-COV-2 in China: impact of public health interventions

10.1101/2020.03.24.20036285 ◽

2020 ◽

Cited By ~ 1

Author(s):

Wenbao Wang ◽

Yiqin Chen ◽

Qi Wang ◽

Ping Cai ◽

Ye He ◽

...

Keyword(s):

Public Health ◽

Health Interventions ◽

Reproductive Number ◽

Public Health Interventions ◽

The Public ◽

Global Pandemic ◽

Actual Growth ◽

Global Threat ◽

The Impact

AbstractCOVID-19 has become a global pandemic. However, the impact of the public health interventions in China needs to be evaluated. We established a SEIRD model to simulate the transmission trend of China. In addition, the reduction of the reproductive number was estimated under the current forty public health interventions policies. Furthermore, the infection curve, daily transmission replication curve, and the trend of cumulative confirmed cases were used to evaluate the effects of the public health interventions. Our results showed that the SEIRD curve model we established had a good fit and the basic reproductive number is 3.38 (95% CI, 3.25–3.48). The SEIRD curve show a small difference between the simulated number of cases and the actual number; the correlation index (H2) is 0.934, and the reproductive number (R) has been reduced from 3.38 to 0.5 under the current forty public health interventions policies of China. The actual growth curve of new cases, the virus infection curve, and the daily transmission replication curve were significantly going down under the current public health interventions. Our results suggest that the current public health interventions of China are effective and should be maintained until COVID-19 is no longer considered a global threat.