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Fulltext Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan)

Khan A, Zarin R, Hussain G, Ahmad NA, Mohd MH, Yusuf A

Results Phys, 2021 Jan;20:103703.
PMID: 33520623 DOI: 10.1016/j.rinp.2020.103703

The dynamic of covid-19 epidemic model with a convex incidence rate is studied in this article. First, we formulate the model without control and study all the basic properties and results including local and global stability. We show the global stability of disease free equilibrium using the method of Lyapunov function theory while for disease endemic, we use the method of geometrical approach. Furthermore, we develop a model with suitable optimal control strategies. Our aim is to minimize the infection in the host population. In order to do this, we use two control variables. Moreover, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behavior of the system. Taking into account the central manifold theory the bifurcation analysis is also incorporated. The numerical simulations are performed in order to show the feasibility of the control strategy and effectiveness of the theoretical results.

Matched MeSH terms: Basic Reproduction Number
A Mathematical Model of the Tuberculosis Epidemic

Ayinla AY, Othman WAM, Rabiu M

Acta Biotheor, 2021 Sep;69(3):225-255.
PMID: 33877474 DOI: 10.1007/s10441-020-09406-8

Tuberculosis has continued to retain its title as "the captain among these men of death". This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals (SDG) and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the model formulation comprising of the susceptible S, vaccinated V, exposed E, undiagnosed infectious I1, diagnosed infectious I2, treated T and recovered R. The stability analysis of the model was established as well as the condition for the model to undergo backward bifurcation. With the existence of backward bifurcation, keeping the basic reproduction number less than unity [Formula: see text] is no more sufficient to keep TB out of the community. Hence, it is shown by the analysis that vaccination program, diagnosis and treatment helps to control the TB dynamics. In furtherance to that, it is shown that preference should be given to diagnosis over treatment as diagnosis precedes treatment. It is as well shown that at lower vaccination rate (0-20%), TB would still be endemic in the population. As such, high vaccination rate is required to send TB out of the community.

Matched MeSH terms: Basic Reproduction Number
Airborne transmission of SARS-CoV-2 is the dominant route of transmission: droplets and aerosols

Rabaan AA, Al-Ahmed SH, Al-Malkey M, Alsubki R, Ezzikouri S, Al-Hababi FH, et al.

Infez Med, 2021 03 01;29(1):10-19.
PMID: 33664169

Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has become a pandemic worldwide. On a daily basis the number of deaths associated with COVID-19 is rapidly increasing. The main transmission route of SARS-CoV-2 is through the air (airborne transmission). This review details the airborne transmission of SARS-CoV-2, the aerodynamics, and different modes of transmission (e.g. droplets, droplet nuclei, and aerosol particles). SARS-CoV-2 can be transmitted by an infected person during activities such as expiration, coughing, sneezing, and talking. During such activities and some medical procedures, aerosols and droplets contaminated with SARS-CoV-2 particles are formed. Depending on their sizes and the environmental conditions, such particles stay viable in the air for varying time periods and can cause infection in a susceptible host. Very few studies have been conducted to establish the mechanism or the aerodynamics of virus-loaded particles and droplets in causing infection. In this review we discuss the various forms in which SARS-CoV-2 virus particles can be transmitted in air and cause infections.

Matched MeSH terms: Basic Reproduction Number/statistics & numerical data
Fulltext Fractal-Fractional Mathematical Model Addressing the Situation of Corona Virus in Pakistan

Shah K, Arfan M, Mahariq I, Ahmadian A, Salahshour S, Ferrara M

Results Phys, 2020 Dec;19:103560.
PMID: 33200064 DOI: 10.1016/j.rinp.2020.103560

This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order

SIR

type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.

Matched MeSH terms: Basic Reproduction Number
Fulltext Measuring Time-Varying Effective Reproduction Numbers for COVID-19 and Their Relationship with Movement Control Order in Malaysia

Musa KI, Arifin WN, Mohd MH, Jamiluddin MS, Ahmad NA, Chen XW, et al.

Int J Environ Res Public Health, 2021 03 22;18(6).
PMID: 33809958 DOI: 10.3390/ijerph18063273

To curb the spread of SARS-CoV-2 virus (COVID-19) in Malaysia, the government imposed a nationwide movement control order (MCO) from 18 March 2020 to 3 May 2020. It was enforced in four phases (i.e., MCO 1, MCO 2, MCO 3 and MCO 4). In this paper, we propose an initiative to assess the impact of MCO by using time-varying reproduction number (Rt). We used data from the Johns Hopkins University Centre for Systems Science and Engineering Coronavirus repository. Day 1 was taken from the first assumed local transmission of COVID-19. We estimated Rt by using the EpiEstim package and plotted the epidemic curve and Rt. Then, we extracted the mean Rt at day 1, day 5 and day 10 for all MCO phases and compared the differences. The Rt values peaked around day 43, which was shortly before the start of MCO 1. The means for Rt at day 1, day 5, and day 10 for all MCOs ranged between 0.665 and 1.147. The average Rt gradually decreased in MCO 1 and MCO 2. Although spikes in the number of confirmed cases were observed when restrictions were gradually relaxed in the later MCO phases, the situation remained under control with Rt values being stabilised to below unity level (Rt value less than one).

Matched MeSH terms: Basic Reproduction Number
Fulltext Transmission dynamics of Zika virus incorporating harvesting

Yue ZM, Yusof FM, Shafie S

Math Biosci Eng, 2020 09 15;17(5):6181-6202.
PMID: 33120594 DOI: 10.3934/mbe.2020327

In this paper, we establish a ZIKV model and investigate the transmission dynamics of ZIKV with two types of harvesting: proportional harvesting and constant harvesting, and give the stability of the steady states of both disease-free and endemic equilibrium, analyze the effect of harvesting on ZIKV transmission dynamics via numerical simulation. We find that proportional harvesting strategy can eliminate the virus when the basic reproduction number $R_0$ is less than 1, but the constant harvesting strategy may control the virus whether the basic reproduction number is less than 1 or not. Epidemiologically, we find that increasing harvesting may stimulate an increase in the number of virus infections at some point, and harvesting can postpone the peak of disease transmission with the mortality of mosquito increasing. The results can provide us with some useful control strategies to regulate ZIKV dynamics.

Matched MeSH terms: Basic Reproduction Number
Fulltext Unravelling the myths of R0 in controlling the dynamics of COVID-19 outbreak: A modelling perspective

Mohd MH, Sulayman F

Chaos Solitons Fractals, 2020 Sep;138:109943.
PMID: 32834577 DOI: 10.1016/j.chaos.2020.109943

COVID-19 is an emerging and rapidly evolving pandemic around the world, which causes severe acute respiratory syndrome and results in substantial morbidity and mortality. To examine the transmission dynamics of COVID-19, we investigate the spread of this pandemic using Malaysia as a case study and scrutinise its interactions with some exogenous factors such as limited medical resources and false detection problems. To do this, we employ a simple epidemiological model and analyse this system using modelling and dynamical systems techniques. We discover some contrasting findings with respect to the observations of basic reproduction number: while it is observed that R0 seems to provide a good description of transmission dynamics in simple outbreak scenarios, this quantity might mislead the assessment on the severity of pandemic when certain complexities such as limited medical resources and false detection problems are incorporated into the model. In particular, we observe the possibility of a COVID-19 outbreak through bistable behaviour, even when the basic reproduction number is less than unity. Based on these findings, we caution policy makers not to make their decisions solely based on the guidance of the basic reproduction number only, which clearly could cause trouble.

Matched MeSH terms: Basic Reproduction Number
Fulltext An analysis of a nonlinear susceptible-exposed-infected-quarantine-recovered pandemic model of a novel coronavirus with delay effect

Raza A, Ahmadian A, Rafiq M, Salahshour S, Ferrara M

Results Phys, 2021 Feb;21:103771.
PMID: 33391985 DOI: 10.1016/j.rinp.2020.103771

In the present study, a nonlinear delayed coronavirus pandemic model is investigated in the human population. For study, we find the equilibria of susceptible-exposed-infected-quarantine-recovered model with delay term. The stability of the model is investigated using well-posedness, Routh Hurwitz criterion, Volterra Lyapunov function, and Lasalle invariance principle. The effect of the reproduction number on dynamics of disease is analyzed. If the reproduction number is less than one then the disease has been controlled. On the other hand, if the reproduction number is greater than one then the disease has become endemic in the population. The effect of the quarantine component on the reproduction number is also investigated. In the delayed analysis of the model, we investigated that transmission dynamics of the disease is dependent on delay terms which is also reflected in basic reproduction number. At the end, to depict the strength of the theoretical analysis of the model, computer simulations are presented.

Matched MeSH terms: Basic Reproduction Number
Fulltext Modelling infectious diseases with herd immunity in a randomly mixed population

Law KB, M Peariasamy K, Mohd Ibrahim H, Abdullah NH

Sci Rep, 2021 10 18;11(1):20574.
PMID: 34663839 DOI: 10.1038/s41598-021-00013-2

The conventional susceptible-infectious-recovered (SIR) model tends to magnify the transmission dynamics of infectious diseases, and thus the estimated total infections and immunized population may be higher than the threshold required for infection control and eradication. The study developed a new SIR framework that allows the transmission rate of infectious diseases to decline along with the reduced risk of contact infection to overcome the limitations of the conventional SIR model. Two new SIR models were formulated to mimic the declining transmission rate of infectious diseases at different stages of transmission. Model A utilized the declining transmission rate along with the reduced risk of contact infection following infection, while Model B incorporated the declining transmission rate following recovery. Both new models and the conventional SIR model were then used to simulate an infectious disease with a basic reproduction number (r0) of 3.0 and a herd immunity threshold (HIT) of 0.667 with and without vaccination. Outcomes of simulations were assessed at the time when the total immunized population reached the level predicted by the HIT, and at the end of simulations. Further, all three models were used to simulate the transmission dynamics of seasonal influenza in the United States and disease burdens were projected and compared with estimates from the Centers for Disease Control and Prevention. For the simulated infectious disease, in the initial phase of the outbreak, all three models performed expectedly when the sizes of infectious and recovered populations were relatively small. As the infectious population increased, the conventional SIR model appeared to overestimate the infections even when the HIT was achieved in all scenarios with and without vaccination. For the same scenario, Model A appeared to attain the level predicted by the HIT and in comparison, Model B projected the infectious disease to be controlled at the level predicted by the HIT only at high vaccination rates. For infectious diseases with high r0, and at low vaccination rates, the level at which the infectious disease was controlled cannot be accurately predicted by the current theorem. Transmission dynamics of infectious diseases with herd immunity can be accurately modelled by allowing the transmission rate of infectious diseases to decline along with the reduction of contact infection risk after recovery or vaccination. Model B provides a credible framework for modelling infectious diseases with herd immunity in a randomly mixed population.

Matched MeSH terms: Basic Reproduction Number
Fulltext Modelling the Effect of a Novel Autodissemination Trap on the Spread of Dengue in Shah Alam and Malaysia

Liang Y, Ahmad Mohiddin MN, Bahauddin R, Hidayatul FO, Nazni WA, Lee HL, et al.

Comput Math Methods Med, 2019;2019:1923479.
PMID: 31481976 DOI: 10.1155/2019/1923479

In this paper, we will start off by introducing the classical Ross-Macdonald model for vector-borne diseases which we use to describe the transmission of dengue between humans and Aedes mosquitoes in Shah Alam, which is a city and the state capital of Selangor, Malaysia. We will focus on analysing the effect of using the Mosquito Home System (MHS), which is an example of an autodissemination trap, in reducing the number of dengue cases by changing the Ross-Macdonald model. By using the national dengue data from Malaysia, we are able to estimate λ, which represents the initial growth rate of the dengue epidemic, and this allows us to estimate the number of mosquitoes in Malaysia. A mathematical expression is also constructed which allows us to estimate the potential number of breeding sites of Aedes mosquitoes. By using the data available from the MHS trial carried out in Section 15 of Shah Alam, we included the potential effect of the MHS into the dengue model and thus modelled the impact MHS has on the spread of dengue within the trial area. We then extended our results to analyse the effect of the MHSs on reducing the number of dengue cases in the whole of Malaysia. A new model was constructed with a basic reproduction number, R0,MalaMHS, which allows us to identify the required MHSs coverage needed to achieve extinction in Malaysia. Numerical simulations and tables of results were also produced to illustrate our results.

Matched MeSH terms: Basic Reproduction Number/statistics & numerical data
Fulltext Modelling the effect of temperature change on the extrinsic incubation period and reproductive number of Plasmodium falciparum in Malaysia

Chua TH

Trop Biomed, 2012 Mar;29(1):121-8.
PMID: 22543612 MyJurnal

According to the report of the Intergovernmental Panel on Climate Change (IPCC), Malaysia will experience an increase of 3-5°C in the future. As the development of the malaria parasite, Plasmodium falciparum, is sensitive to temperature, we investigated, using computer models, the effect of increase of 3º and 5ºC on the possible changes in the epidemiology of malaria transmission of P. falciparum in Malaysia. Four environmentally different locations were selected: Kuala Lumpur (KL), Cameron Highlands (CH), Kota Kinabalu (KK) and Kinabalu Park (KP). The extrinsic incubation period (EIP) was estimated using hourly temperatures and the mean daily temperatures. The EIP values estimated using the mean daily temperature were lower than those computed from hourly temperatures in warmer areas (KL, KK), but higher in the cooler areas (CH, KP). The computer simulations also indicated that the EIP will be decreased if the temperature was raised by 3º or 5ºC, with the effect more pronounced for the greater temperature increase, and for the cooler places. The vector cohort that is still alive at a time to transmit malaria (s(EIP)) also increased when the temperature was raised, with the increase more pronounced in the cooler areas. This study indicates an increase in temperature will have more significant effect in shortening the EIP in a cooler place (eg CH, KP), resulting in a greater s(EIP), and consequently increasing the transmission intensity and malaria risk. A temperature increase arising from the global climate change will likely affect the epidemiology of malaria in Malaysia, especially in the cooler areas.

Matched MeSH terms: Basic Reproduction Number
Fulltext Using routine surveillance data to estimate the epidemic potential of emerging zoonoses: application to the emergence of US swine origin influenza A H3N2v virus

Cauchemez S, Epperson S, Biggerstaff M, Swerdlow D, Finelli L, Ferguson NM

PLoS Med, 2013;10(3):e1001399.
PMID: 23472057 DOI: 10.1371/journal.pmed.1001399

BACKGROUND: Prior to emergence in human populations, zoonoses such as SARS cause occasional infections in human populations exposed to reservoir species. The risk of widespread epidemics in humans can be assessed by monitoring the reproduction number R (average number of persons infected by a human case). However, until now, estimating R required detailed outbreak investigations of human clusters, for which resources and expertise are not always available. Additionally, existing methods do not correct for important selection and under-ascertainment biases. Here, we present simple estimation methods that overcome many of these limitations.
METHODS AND FINDINGS: Our approach is based on a parsimonious mathematical model of disease transmission and only requires data collected through routine surveillance and standard case investigations. We apply it to assess the transmissibility of swine-origin influenza A H3N2v-M virus in the US, Nipah virus in Malaysia and Bangladesh, and also present a non-zoonotic example (cholera in the Dominican Republic). Estimation is based on two simple summary statistics, the proportion infected by the natural reservoir among detected cases (G) and among the subset of the first detected cases in each cluster (F). If detection of a case does not affect detection of other cases from the same cluster, we find that R can be estimated by 1-G; otherwise R can be estimated by 1-F when the case detection rate is low. In more general cases, bounds on R can still be derived.
CONCLUSIONS: We have developed a simple approach with limited data requirements that enables robust assessment of the risks posed by emerging zoonoses. We illustrate this by deriving transmissibility estimates for the H3N2v-M virus, an important step in evaluating the possible pandemic threat posed by this virus. Please see later in the article for the Editors' Summary.

Matched MeSH terms: Basic Reproduction Number

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