Optimal Control of SIRS Model with Limited Medical Resources and Reinfection Problems

COVID-19 is a global public health problem that causes severe acute respiratory syndrome (SARS). It is also extremely contagious with rapidly increasing death rates. In this paper, we propose an optimal control model with SIRS (Susceptible–Infected–Recovered- Susceptible) kinetics to examine the effects of several intervention measures (e.g., vaccination and treatment) under the limited medical resources scenarios. This model is also employed to investigate the possibility of reinfection because of the fading of immunity problem. As a case study, the modeling framework is parametrised using COVID-19 daily confirmed and recovered cases in Malaysia. The parameters have been approximated by relying on the model's best fit to actual data published by the Malaysian Ministry of Health (MOH). Our numerical simulation results show that the inclusion of optimal control components with vaccination and treatment strategies would dramatically reduce the number of active cases even in the presence of reinfection forces. Regardless of the relative weightage (or costs) of vaccination and treatment, as well as the possibility of reinfection, it is critical to plan effective COVID-19 control measures by vaccinating as many people as possible (and as early as possible). Overall, these insights help explore the importance of intervention measures and the allocation of medical resources to control the severity of this pandemic.

Dynamical System Analysis of the Prey-predator Interactions involving Prey Refuge and Herd Behaviors in Preys

By employing a prey refuge mechanism, more preys can be protected from predation. Prey species are also better protected from predation when they congregate in herds. However, what if the prey refuge and herd behavior mechanisms were combined in a system? To investigate this phenomenon, we consider two different prey-predator systems with prey refuge capacity. The first system is a simple prey-predator with prey refuge, whereas the second system considers prey refuge and prey herd behavior mechanisms. Using these models, we explore how different prey refuge strategies affect species interactions in both systems. To accomplish this, we use theoretical techniques (e.g., computing steady states and performing the stability analysis) and numerical bifurcation analysis to demonstrate various dynamical behaviors of these two prey-predator systems. Once prey refuge is treated as a bifurcation parameter, we observe the occurrence of supercritical Hopf and transcritical bifurcations in both systems. Furthermore, we explore the dynamic effects of prey refuge and predator handling time on species population interactions: our findings reveal that using both prey refuge and herd behavior as escape strategies; it is possible to dilute the predation pressure and ensure species biodiversity.

Joint Effects of Dispersal and Trophic Interactions on the Biodiversity of Species

Local dispersal and trophic interactions are thought to have important influences on species range limits (i.e., the boundaries of locations where species is found) across geographical regions. To better understand this problem, we perform a numerical bifurcation analysis of a partial differential equations model. This system consists of prey-predator interactions, environmental suitability, and local dispersal terms. The main objective of this investigation is to examine the combined effects of distinct ecological factors on species population dynamics. In the absence of dispersal, our results show that variations in abiotic environments and handling times of predator lead to different outcomes of species interactions (i.e., stable limit cycles, species coexistence, and species exclusion). The inclusion of dispersal into this system reduces the predation pressure and stabilizes this ecological community to mediate species biodiversity. Local dispersal also induces intriguing dynamical behaviour in the system such as bistability and unstable limit cycles. 

Modelling COVID-19 Scenarios for the States and Federal Territories of Malaysia

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causes COVID-19 disease, which has become pandemic since December 2019. In the recent months, among five countries in the Southeast Asia, Malaysia has the highest per-capita daily new cases and daily new deaths. A mathematical modelling approach using a Singular Spectrum Analysis (SSA) technique was used to generate data-driven 30-days ahead forecasts for the number of daily cases in the states and federal territories in Malaysia at four consecutive time points between 27 July 2021 and 26 August 2021. Each forecast was produced using SSA prediction model of the current major trend at each time point. The objective is to understand the transition dynamics of COVID-19 in each state by analysing the direction of change of the major trends during the period of study. The states and federal territories in Malaysia were grouped in four categories based on the nature of the transition. Overall, it was found that the COVID-19 spread has progressed unevenly across states and federal territories. Major regions like Selangor, Kuala Lumpur, Putrajaya and Negeri Sembilan were in Group 3 (fast decrease in infectivity) and Labuan was in Group 4 (possible eradication of infectivity). Other states e.g. Pulau Pinang, Sabah, Sarawak, Kelantan and Johor were categorised in Group 1 (very high infectivity levels) with Perak, Kedah, Pahang, Terengganu and Melaka were classified in Group 2 (high infectivity levels). It is also cautioned that SSA provides a promising avenue for forecasting the transition dynamics of COVID-19; however, the reliability of this technique depends on the availability of good quality data.

Internal phosphorus recycling promotes rich and complex dynamics in an algae-phosphorus model: Implications for eutrophication management

Internal phosphorus recycling in lakes is an important nutrient source that promotes algal growth. Its persistence impedes the effort to improve water quality and thus poses a challenge to the management of eutrophication in lakes, especially in shallow lakes where the occurrence of internal phosphorus recycling is reportedly more common. This paper aims to provide crucial insights on the effects of internal phosphorus recycling on eutrophication dynamics for effective management of lake eutrophication. For this purpose, a mathematical model for lake eutrophication, comprising two compartments of algae and phosphorus, is first formulated for application to a eutrophic tropical lake named Tasik Harapan in Universiti Sains Malaysia. Numerical bifurcation analysis of the model is then performed to assess the combined influences of internal phosphorus recycling, algal mortality and external phosphorus loading on Tasik Harapan eutrophication dynamics. Specifically, co-dimension one bifurcation analysis of algal mortality rate is carried out by means of XPPAUT for various external phosphorus loading rates. The emergence of limit cycle for a certain range of algal mortality rate could be related to the hydra effect (i.e., algal concentration increases in response to greater algal mortality) and the paradox of enrichment (i.e., destabilization of algae in nutrient rich environment). To trace the locus of co-dimension one bifurcation, co-dimension two bifurcation analysis is performed by means of MatCont. The analysis demonstrated that the inclusion of the internal phosphorus recycling term induces rich and complex dynamics of the model. These dynamics include saddle-node bifurcation, cusp, Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and limit point bifurcation of cycles. The results suggest that high internal phosphorus recycling rate promotes bistability and catastrophic shift in a shallow and tropical lake like Tasik Harapan. Hence, the key to effective management of eutrophication in shallow and tropical lakes is the control of internal phosphorus recycling.

Situational Analysis for COVID-19: Estimating Transmission Dynamics in Malaysia using an SIR-Type Model with Neural Network Approach

COVID-19 is a major health threat across the globe, which causes severe acute respiratory syndrome, and it is highly contagious with significant morbidity and mortality. In this paper, we examine the feasibility and implications of several phases of Movement Control Order (MCO) and some non-pharmaceutical intervention (NPI) strategies implemented by Malaysian government in the year 2020 using a mathematical model with SIR-neural network approaches. It is observed that this model is able to mimic the trend of infection trajectories of COVID-19 pandemic and, Malaysia had succeeded to flatten the infection curve at the end of the Conditional MCO (CMCO) period. However, the signs of ‘flattening’ with R0 of less than one had been taken as a signal to ease up on some restrictions enforced before. Though the government has made compulsory the use of face masks in public places to control the spread of COVID-19, we observe a contrasting finding from our model with regards to the impacts of wearing mask policies in Malaysia on R0 and the infection curve. Additionally, other events such as the Sabah State Election at the end of third quarter of 2020 has also imposed a dramatic COVID-19 burden on the society and the healthcare systems.

Scenario analysis of COVID-19 transmission dynamics in Malaysia with the possibility of reinfection and limited medical resources scenarios

COVID-19 is a major health threat across the globe, which causes severe acute respiratory syndrome (SARS), and it is highly contagious with significant mortality. In this study, we conduct a scenario analysis for COVID-19 in Malaysia using a simple universality class of the SIR system and extensions thereof (i.e., the inclusion of temporary immunity through the reinfection problems and limited medical resources scenarios leads to the SIRS-type model). This system has been employed in order to provide further insights on the long-term outcomes of COVID-19 pandemic. As a case study, the COVID-19 transmission dynamics are investigated using daily confirmed cases in Malaysia, where some of the epidemiological parameters of this system are estimated based on the fitting of the model to real COVID-19 data released by the Ministry of Health Malaysia (MOH). We observe that this model is able to mimic the trend of infection trajectories of COVID-19 pandemic in Malaysia and it is possible for transmission dynamics to be influenced by the reinfection force and limited medical resources problems. A rebound effect in transmission could occur after several years and this situation depends on the intensity of reinfection force. Our analysis also depicts the existence of a critical value in reinfection threshold beyond which the infection dynamics persist and the COVID-19 outbreaks are rather hard to eradicate. Therefore, understanding the interplay between distinct epidemiological factors using mathematical modelling approaches could help to support authorities in making informed decisions so as to control the spread of this pandemic effectively.

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

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.

Combined Impacts of Predation, Mutualism and Dispersal on the Dynamics of a Four-Species Ecological System

Multi-species and ecosystem models have provided ecologist with an excellent opportunity to study the effects of multiple biotic interactions in an ecological system. Predation and mutualism are among the most prevalent biotic interactions in the multi-species system. Several ecological studies exist, but they are based on one-or two-species interactions, and in real life, multiple interactions are natural characteristics of a multi-species community. Here, we use a system of partial differential equations to study the combined effects of predation, mutualism and dispersal on the multi-species coexistence and community stability in the ecological system. Our results show that predation provided a defensive mechanism against the negative consequences of the multiple species interactions by reducing the net effect of competition. Predation is critical in the stability and coexistence of the multi-species community. The combined effects of predation and dispersal enhance the multiple species coexistence and persistence. Dispersal exerts a positive effect on the system by supporting multiple species coexistence and stability of community structures. Dispersal process also reduces the adverse effects associated with multiple species interactions. Additionally, mutualism induces oscillatory behaviour on the system through Hopf bifurcation. The roles of mutualism also support multiple species coexistence mechanisms (for some threshold values) by increasing the stable coexistence and the stable limit cycle regions. We discover that the stability and coexistence mechanisms are controlled by the transcritical and Hopf bifurcation that occurs in this system. Most importantly, our results show the important influences of predation, mutualism and dispersal in the stability and coexistence of the multi-species communities

Identification of Botryosphaeriaceae associated with stem-end rot of mango (Mangifera indica L.) in Malaysia

AIMS

To identify Botryosphaeriaceae fungal species that are associated with stem-end rot of mango, and to study their pathogenicity on mango fruit.

METHODS AND RESULTS

Based on the sequences of internal transcribed spacer (ITS), TEF1-α and β-tubulin, as well as on the phylogenetic analysis of combined sequences, four species of Lasiodiplodia (L. theobromae,L. pseudotheobromae, L. iranensis, L. mahajangana) and two species of Neofusicoccum (N. ribis, N. parvum) were identified. Pseudofusicoccum violaceum, Neoscytalidium dimidiatum and three species of Botryosphaeria (B. scharifii, B. dothidea, B. ramosa) were identified based on sequences of ITS and TEF1-α. Pathogenicity test of selected isolates were tested on Chok Anan, Waterlily and Falan mango cultivars. Generally, all species were observed to be pathogenic on the three tested mango cultivars on wounded fruits, except for N. ribis and N. parvum, which were pathogenic on both wounded and unwounded fruits. However, N. ribis was only pathogenic on cultivar Falan, whereas B. ramosa were pathogenic on cultivars Waterlily and Falan.

CONCLUSIONS

Eleven species of Botryosphaeriaceae were associated with mango stem-end rot in Malaysia. To the best of our knowledge, four species, namely L. mahajangana, B. ramosa, N. ribis and P. violaceum are the first recorded Botryosphaeriaceae fungi associated with stem end rot of mango.

SIGNIFICANCE AND IMPACT OF THE STUDY

The identification of Botryosphaeriaceae fungi is important to establish suitable control measures and quarantine requirements. Many species have a wide host range, which means that there is a possibility of cross infection from other infected plants.

Unravelling the myths of R 0 in controlling the dynamics of COVID-19 outbreak: A modelling perspective

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 R ₀ 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.

Identification, pathogenicity and histopathology of Colletotrichum sansevieriae causing anthracnose of Sansevieria trifasciata in Malaysia

AIMS

To characterize causal pathogen of Sansevieria trifasciata anthracnose through morphology and molecular analysis; to evaluate the host range of the pathogen; and to explicate the infection process by the pathogen histopathologically.

METHODS AND RESULTS

Symptomatic leaves of S. trifasciata were collected from five states in Malaysia. The causal pathogen was isolated and identified for the first time in Malaysia as C. sansevieriae based on morphological and multi-gene phylogenetic analyses using ITS, TUB2 and GAPDH sequences. Pathogenicity tests were conducted on different hosts. Colletotrichum sansevieriae was not pathogenic towards S. cylindrica, S. masoniana, Furcraea foetida, Chlorophytum comosum, Aloe vera and Gasteria carinata, confirming the exceptionally high host specificity for a species of Colletotrichum. Histopathology was performed using light microscope and scanning electron microscopy to study the infection process of C. sansevieriae on S. trifasciata. Colonization of host leaves by the pathogen was observed 2 days after inoculation.

CONCLUSIONS

Colletotrichum sansevieriae caused anthracnose of S. trifasciata in Malaysia. It is a host-specific pathogen and colonized the host intracellularly.

SIGNIFICANCE AND IMPACT OF THE STUDY

This is the first report of C. sansevieriae causing anthracnose of S. trifasciata in Malaysia. The host range test and understanding of the infection process will provide better understanding of the host-pathogen relationship and beneficial for effective disease management.